Continuous frequency distribution of infinite range. Its properties are as follows: 1, continuous, symmetrical distribution with both tails extending to infinity; 2, arithmetic mean, mode, and median identical; and 3, shape completely determined by the mean and standard deviation.
A quinolizidine alkaloid isolated from several FABACEAE including LUPINUS; SPARTIUM; and CYTISUS. It has been used as an oxytocic and an anti-arrhythmia agent. It has also been of interest as an indicator of CYP2D6 genotype.
The complete summaries of the frequencies of the values or categories of a measurement made on a group of items, a population, or other collection of data. The distribution tells either how many or what proportion of the group was found to have each value (or each range of values) out of all the possible values that the quantitative measure can have.
Statistical formulations or analyses which, when applied to data and found to fit the data, are then used to verify the assumptions and parameters used in the analysis. Examples of statistical models are the linear model, binomial model, polynomial model, two-parameter model, etc.
The use of statistical and mathematical methods to analyze biological observations and phenomena.
Application of statistical procedures to analyze specific observed or assumed facts from a particular study.
The probability distribution associated with two mutually exclusive outcomes; used to model cumulative incidence rates and prevalence rates. The Bernoulli distribution is a special case of binomial distribution.
The range or frequency distribution of a measurement in a population (of organisms, organs or things) that has not been selected for the presence of disease or abnormality.
Computer-based representation of physical systems and phenomena such as chemical processes.
A theorem in probability theory named for Thomas Bayes (1702-1761). In epidemiology, it is used to obtain the probability of disease in a group of people with some characteristic on the basis of the overall rate of that disease and of the likelihood of that characteristic in healthy and diseased individuals. The most familiar application is in clinical decision analysis where it is used for estimating the probability of a particular diagnosis given the appearance of some symptoms or test result.
The science and art of collecting, summarizing, and analyzing data that are subject to random variation. The term is also applied to the data themselves and to the summarization of the data.
A procedure consisting of a sequence of algebraic formulas and/or logical steps to calculate or determine a given task.
Theoretical representations that simulate the behavior or activity of genetic processes or phenomena. They include the use of mathematical equations, computers, and other electronic equipment.
In statistics, a technique for numerically approximating the solution of a mathematical problem by studying the distribution of some random variable, often generated by a computer. The name alludes to the randomness characteristic of the games of chance played at the gambling casinos in Monte Carlo. (From Random House Unabridged Dictionary, 2d ed, 1993)
A characteristic showing quantitative inheritance such as SKIN PIGMENTATION in humans. (From A Dictionary of Genetics, 4th ed)
The study of chance processes or the relative frequency characterizing a chance process.
The statistical reproducibility of measurements (often in a clinical context), including the testing of instrumentation or techniques to obtain reproducible results. The concept includes reproducibility of physiological measurements, which may be used to develop rules to assess probability or prognosis, or response to a stimulus; reproducibility of occurrence of a condition; and reproducibility of experimental results.
Genetic loci associated with a QUANTITATIVE TRAIT.
Functions constructed from a statistical model and a set of observed data which give the probability of that data for various values of the unknown model parameters. Those parameter values that maximize the probability are the maximum likelihood estimates of the parameters.
The number of units (persons, animals, patients, specified circumstances, etc.) in a population to be studied. The sample size should be big enough to have a high likelihood of detecting a true difference between two groups. (From Wassertheil-Smoller, Biostatistics and Epidemiology, 1990, p95)
The production of offspring by selective mating or HYBRIDIZATION, GENETIC in animals or plants.
A stochastic process such that the conditional probability distribution for a state at any future instant, given the present state, is unaffected by any additional knowledge of the past history of the system.
Theoretical representations that simulate the behavior or activity of biological processes or diseases. For disease models in living animals, DISEASE MODELS, ANIMAL is available. Biological models include the use of mathematical equations, computers, and other electronic equipment.
Statistical models in which the value of a parameter for a given value of a factor is assumed to be equal to a + bx, where a and b are constants. The models predict a linear regression.
The outward appearance of the individual. It is the product of interactions between genes, and between the GENOTYPE and the environment.
A statistical technique that isolates and assesses the contributions of categorical independent variables to variation in the mean of a continuous dependent variable.
Genotypic differences observed among individuals in a population.
A phenotypically recognizable genetic trait which can be used to identify a genetic locus, a linkage group, or a recombination event.
Elements of limited time intervals, contributing to particular results or situations.
The status during which female mammals carry their developing young (EMBRYOS or FETUSES) in utero before birth, beginning from FERTILIZATION to BIRTH.
Domesticated bovine animals of the genus Bos, usually kept on a farm or ranch and used for the production of meat or dairy products or for heavy labor.
Theoretical representations that simulate the behavior or activity of systems, processes, or phenomena. They include the use of mathematical equations, computers, and other electronic equipment.
Binary classification measures to assess test results. Sensitivity or recall rate is the proportion of true positives. Specificity is the probability of correctly determining the absence of a condition. (From Last, Dictionary of Epidemiology, 2d ed)
Hybridization of a nucleic acid sample to a very large set of OLIGONUCLEOTIDE PROBES, which have been attached individually in columns and rows to a solid support, to determine a BASE SEQUENCE, or to detect variations in a gene sequence, GENE EXPRESSION, or for GENE MAPPING.
Age as a constituent element or influence contributing to the production of a result. It may be applicable to the cause or the effect of a circumstance. It is used with human or animal concepts but should be differentiated from AGING, a physiological process, and TIME FACTORS which refers only to the passage of time.
Microscopy using an electron beam, instead of light, to visualize the sample, thereby allowing much greater magnification. The interactions of ELECTRONS with specimens are used to provide information about the fine structure of that specimen. In TRANSMISSION ELECTRON MICROSCOPY the reactions of the electrons that are transmitted through the specimen are imaged. In SCANNING ELECTRON MICROSCOPY an electron beam falls at a non-normal angle on the specimen and the image is derived from the reactions occurring above the plane of the specimen.
Procedures for finding the mathematical function which best describes the relationship between a dependent variable and one or more independent variables. In linear regression (see LINEAR MODELS) the relationship is constrained to be a straight line and LEAST-SQUARES ANALYSIS is used to determine the best fit. In logistic regression (see LOGISTIC MODELS) the dependent variable is qualitative rather than continuously variable and LIKELIHOOD FUNCTIONS are used to find the best relationship. In multiple regression, the dependent variable is considered to depend on more than a single independent variable.
A set of techniques used when variation in several variables has to be studied simultaneously. In statistics, multivariate analysis is interpreted as any analytic method that allows simultaneous study of two or more dependent variables.
The determination of the pattern of genes expressed at the level of GENETIC TRANSCRIPTION, under specific circumstances or in a specific cell.
Any detectable and heritable change in the genetic material that causes a change in the GENOTYPE and which is transmitted to daughter cells and to succeeding generations.
Cells propagated in vitro in special media conducive to their growth. Cultured cells are used to study developmental, morphologic, metabolic, physiologic, and genetic processes, among others.

Personal exposure to dust, endotoxin and crystalline silica in California agriculture. (1/1216)

AIMS: The aim of this study was to measure personal exposure to dust, endotoxin and crystalline silica during various agricultural operations in California over a period of one year. METHODS: Ten farms were randomly selected in Yolo and Solano counties and workers were invited to wear personal sampling equipment to measure inhalable and respirable dust levels during various operations. The samples were analysed for endotoxin using the Limulus Amebocyte Lysate assay and crystalline silica content using X-ray diffraction. In total 142 inhalable samples and 144 respirable samples were collected. RESULTS: The measurements showed considerable difference in exposure levels between various operations, in particular for the inhalable fraction of the dust and the endotoxin. Machine harvesting of tree crops (Geometric mean (GM) = 45.1 mg/m3) and vegetables (GM = 7.9 mg/m3), and cleaning of poultry houses (GM = 6.7 mg/m3) showed the highest inhalable dust levels. Cleaning of poultry houses also showed the highest inhalable endotoxin levels (GM = 1861 EU/m3). Respirable dust levels were generally low, except for machine harvesting of tree crops (GM = 2.8 mg/m3) and vegetables (GM = 0.9 mg/m3). Respirable endotoxin levels were also low. For the inhalable dust fraction, levels were reduced considerably when an enclosed cabin was present. The percentage of crystalline silica was overall higher in the respirable dust samples than the inhalable dust samples. CONCLUSIONS: Considerable differences exist in personal exposure levels to dust, endotoxin and crystalline silica during various agricultural operations in California agriculture with some operations showing very high levels.  (+info)

Functionally independent components of the late positive event-related potential during visual spatial attention. (2/1216)

Human event-related potentials (ERPs) were recorded from 10 subjects presented with visual target and nontarget stimuli at five screen locations and responding to targets presented at one of the locations. The late positive response complexes of 25-75 ERP average waveforms from the two task conditions were simultaneously analyzed with Independent Component Analysis, a new computational method for blindly separating linearly mixed signals. Three spatially fixed, temporally independent, behaviorally relevant, and physiologically plausible components were identified without reference to peaks in single-channel waveforms. A novel frontoparietal component (P3f) began at approximately 140 msec and peaked, in faster responders, at the onset of the motor command. The scalp distribution of P3f appeared consistent with brain regions activated during spatial orienting in functional imaging experiments. A longer-latency large component (P3b), positive over parietal cortex, was followed by a postmotor potential (Pmp) component that peaked 200 msec after the button press and reversed polarity near the central sulcus. A fourth component associated with a left frontocentral nontarget positivity (Pnt) was evoked primarily by target-like distractors presented in the attended location. When no distractors were presented, responses of five faster-responding subjects contained largest P3f and smallest Pmp components; when distractors were included, a Pmp component appeared only in responses of the five slower-responding subjects. Direct relationships between component amplitudes, latencies, and behavioral responses, plus similarities between component scalp distributions and regional activations reported in functional brain imaging experiments suggest that P3f, Pmp, and Pnt measure the time course and strength of functionally distinct brain processes.  (+info)

Haemoglobin and ferritin concentrations in children aged 12 and 18 months. ALSPAC Children in Focus Study Team. (3/1216)

AIMS: To define the normal ranges and investigate associated factors for haemoglobin and ferritin in British children at 12 and 18 months of age, and to estimate correlations between both haemoglobin and ferritin concentrations at 8, 12, and 18 months of age. SUBJECTS AND METHODS: Subjects were part of the "children in focus" sample, randomly selected from the Avon longitudinal study of pregnancy and childhood. Capillary blood samples were taken from 940 children at 12 months and 827 children at 18 months of age. RESULTS: Haemoglobin was distributed normally and ferritin was distributed log normally at 12 and 18 months of age. Ninety five per cent reference ranges were established from empirical centiles of haemoglobin and ferritin. Haemoglobin concentrations at 18 months were associated with sex and maternal education. Concentrations of ferritin at 12 and 18 months of age were associated with birth weight and current weight. Girls at 12 months, but not at 18 months, had 8% higher ferritin concentrations than boys. Haemoglobin and ferritin concentrations were significantly correlated over time (8-12 months: rHb = 0.26, rFer = 0.46; 12-18 months: rHb = 0.37, rFer = 0.34; 8-18 months: rHb = 0.22, rFer = 0.24). CONCLUSION: Iron stores are depleted by rapid growth in infancy. A definition of anaemia based on the fifth centile gives cut off points at 12 and 18 months of age of haemoglobin < 100 g/l, and for iron deficiency of ferritin < 16 micrograms/l and < 12 micrograms/l, respectively. Because children below the fifth centile at one time point differ from those six months later, it is unclear whether screening would be effective.  (+info)

Trace elements and electrolytes in human resting mixed saliva after exercise. (4/1216)

OBJECTIVES: Exercise is known to cause changes in the concentration of salivary components such as amylase, Na, and Cl. The aim of this investigation was to evaluate the effect of physical exercise on the levels of trace elements and electrolytes in whole (mixed) saliva. METHODS: Forty subjects performed a maximal exercise test on a cycle ergometer. Samples of saliva were obtained before and immediately after the exercise test. Sample concentrations of Fe, Mg, Sc, Cr, Mn, Co, Cu, Zn, Se, Sr, Ag, Sb, Cs, and Hg were determined by inductively coupled plasma mass spectrometry and concentrations of Ca and Na by atomic absorption spectrometry. RESULTS: After exercise, Mg and Na levels showed a significant increase (p < 0.05) while Mn levels fell (p < 0.05). Zn/Cu molar ratios were unaffected by exercise. CONCLUSIONS: Intense physical exercise induced changes in the concentrations of only three (Na, Mg, and Mn) of the 16 elements analysed in the saliva samples. Further research is needed to assess the clinical implications of these findings.  (+info)

The photon counting histogram in fluorescence fluctuation spectroscopy. (5/1216)

Fluorescence correlation spectroscopy (FCS) is generally used to obtain information about the number of fluorescent particles in a small volume and the diffusion coefficient from the autocorrelation function of the fluorescence signal. Here we demonstrate that photon counting histogram (PCH) analysis constitutes a novel tool for extracting quantities from fluorescence fluctuation data, i.e., the measured photon counts per molecule and the average number of molecules within the observation volume. The photon counting histogram of fluorescence fluctuation experiments, in which few molecules are present in the excitation volume, exhibits a super-Poissonian behavior. The additional broadening of the PCH compared to a Poisson distribution is due to fluorescence intensity fluctuations. For diffusing particles these intensity fluctuations are caused by an inhomogeneous excitation profile and the fluctuations in the number of particles in the observation volume. The quantitative relationship between the detected photon counts and the fluorescence intensity reaching the detector is given by Mandel's formula. Based on this equation and considering the fluorescence intensity distribution in the two-photon excitation volume, a theoretical expression for the PCH as a function of the number of molecules in the excitation volume is derived. For a single molecular species two parameters are sufficient to characterize the histogram completely, namely the average number of molecules within the observation volume and the detected photon counts per molecule per sampling time epsilon. The PCH for multiple molecular species, on the other hand, is generated by successively convoluting the photon counting distribution of each species with the others. The influence of the excitation profile upon the photon counting statistics for two relevant point spread functions (PSFs), the three-dimensional Gaussian PSF conventionally employed in confocal detection and the square of the Gaussian-Lorentzian PSF for two photon excitation, is explicitly treated. Measured photon counting distributions obtained with a two-photon excitation source agree, within experimental error with the theoretical PCHs calculated for the square of a Gaussian-Lorentzian beam profile. We demonstrate and discuss the influence of the average number of particles within the observation volume and the detected photon counts per molecule per sampling interval upon the super-Poissonian character of the photon counting distribution.  (+info)

Abnormal NF-kappa B activity in T lymphocytes from patients with systemic lupus erythematosus is associated with decreased p65-RelA protein expression. (6/1216)

Numerous cellular and biochemical abnormalities in immune regulation have been described in patients with systemic lupus erythematosus (SLE), including surface Ag receptor-initiated signaling events and lymphokine production. Because NF-kappa B contributes to the transcription of numerous inflammatory genes and has been shown to be a molecular target of antiinflammatory drugs, we sought to characterize the functional role of the NF-kappa B protein complex in lupus T cells. Freshly isolated T cells from lupus patients, rheumatoid arthritis (RA) patients, and normal individuals were activated physiologically via the TCR with anti-CD3 and anti-CD28 Abs to assess proximal membrane signaling, and with PMA and a calcium ionophore (A23187) to bypass membrane-mediated signaling events. We measured the NF-kappa B binding activity in nuclear extracts by gel shift analysis. When compared with normal cells, the activation of NF-kappa B activity in SLE patients was significantly decreased in SLE, but not in RA, patients. NF-kappa B binding activity was absent in several SLE patients who were not receiving any medication, including corticosteroids. Also, NF-kappa B activity remained absent in follow-up studies. In supershift experiments using specific Abs, we showed that, in the group of SLE patients who displayed undetectable NF-kappa B activity, p65 complexes were not formed. Finally, immunoblot analysis of nuclear extracts showed decreased or absent p65 protein levels. As p65 complexes are transcriptionally active in comparison to the p50 homodimer, this novel finding may provide insight on the origin of abnormal cytokine or other gene transcription in SLE patients.  (+info)

Integrated screening for Down's syndrome on the basis of tests performed during the first and second trimesters. (7/1216)

BACKGROUND: Both first-trimester screening and second-trimester screening for Down's syndrome are effective means of selecting women for chorionic-villus sampling or amniocentesis, but there is uncertainty about which screening method should be used in practice. We propose a new screening method in which measurements obtained during both trimesters are integrated to provide a single estimate of a woman's risk of having a pregnancy affected by Down's syndrome. METHODS: We used data from published studies of various screening methods employed during the first and second trimesters. The first-trimester screening consisted of measurement of serum pregnancy-associated plasma protein A in 77 pregnancies affected by Down's syndrome and 383 unaffected pregnancies and measurements of nuchal translucency obtained by ultrasonography in 326 affected and 95,476 unaffected pregnancies. The second-trimester tests were various combinations of measurements of serum alpha-fetoprotein, unconjugated estriol, human chorionic gonadotropin, and inhibin A in 77 affected and 385 unaffected pregnancies. RESULTS: When we used a risk of 1 in 120 or greater as the cutoff to define a positive result on the integrated screening test, the rate of detection of Down's syndrome was 85 percent, with a false positive rate of 0.9 percent. To achieve the same rate of detection, current screening tests would have higher false positive rates (5 to 22 percent). If the integrated test were to replace the triple test (measurements of serum alpha-fetoprotein, unconjugated estriol, and human chorionic gonadotropin), currently used with a 5 percent false positive rate, for screening during the second trimester, the detection rate would be higher 85 percent vs. 69 percent), with a reduction of four fifths in the number of invasive diagnostic procedures and consequent losses of normal fetuses. CONCLUSIONS: The integrated test detects more cases of Down's syndrome with a much lower false positive rate than the best currently available test.  (+info)

Microtubule-dependent recruitment of Staufen-green fluorescent protein into large RNA-containing granules and subsequent dendritic transport in living hippocampal neurons. (8/1216)

Dendritic mRNA transport and local translation at individual potentiated synapses may represent an elegant way to form synaptic memory. Recently, we characterized Staufen, a double-stranded RNA-binding protein, in rat hippocampal neurons and showed its presence in large RNA-containing granules, which colocalize with microtubules in dendrites. In this paper, we transiently transfect hippocampal neurons with human Staufen-green fluorescent protein (GFP) and find fluorescent granules in the somatodendritic domain of these cells. Human Stau-GFP granules show the same cellular distribution and size and also contain RNA, as already shown for the endogenous Stau particles. In time-lapse videomicroscopy, we show the bidirectional movement of these Staufen-GFP-labeled granules from the cell body into dendrites and vice versa. The average speed of these particles was 6.4 microm/min with a maximum velocity of 24. 3 microm/min. Moreover, we demonstrate that the observed assembly into granules and their subsequent dendritic movement is microtubule dependent. Taken together, we have characterized a novel, nonvesicular, microtubule-dependent transport pathway involving RNA-containing granules with Staufen as a core component. This is the first demonstration in living neurons of movement of an essential protein constituent of the mRNA transport machinery.  (+info)

To the best of my knowledge, "Normal Distribution" is not a term that has a specific medical definition. It is a statistical concept that describes a distribution of data points in which the majority of the data falls around a central value, with fewer and fewer data points appearing as you move further away from the center in either direction. This type of distribution is also known as a "bell curve" because of its characteristic shape.

In medical research, normal distribution may be used to describe the distribution of various types of data, such as the results of laboratory tests or patient outcomes. For example, if a large number of people are given a particular laboratory test, their test results might form a normal distribution, with most people having results close to the average and fewer people having results that are much higher or lower than the average.

It's worth noting that in some cases, data may not follow a normal distribution, and other types of statistical analyses may be needed to accurately describe and analyze the data.

Sparteine is not typically referred to as a "medical definition" in the context of modern medicine. However, it is a chemical compound with some historical use in medicine and a well-defined chemical structure.

Here's a chemical definition of sparteine:

Sparteine is an alkaloid derived from plants of the genus *Colutea* and *Genista*, but most notably from *Crotalaria sagittalis* (rattlebox) and *Echium plantagineum* (viper's bugloss). Its chemical formula is C15H24N2, and it has a molecular weight of 228.36 g/mol.

Sparteine is a stereoisomer of lupanine and is structurally related to other natural alkaloids such as nicotine and coniine. It is a chiral compound with two stereocenters, existing as four different stereoisomers: (−)-sparteine, (+)-sparteine, (−)-pseudosparteine, and (+)-pseudosparteine.

Historically, sparteine has been used in medicine as a cardiotonic, uterine stimulant, and antispasmodic. However, due to its narrow therapeutic index and the availability of safer alternatives, it is no longer in common clinical use today.

In medical statistics, a statistical distribution refers to the pattern of frequency or proportion of certain variables in a population. It describes how the data points in a sample are distributed and can be used to make inferences about a larger population. There are various types of statistical distributions, including normal (or Gaussian) distribution, binomial distribution, Poisson distribution, and exponential distribution, among others. These distributions have specific mathematical properties that allow researchers to calculate probabilities and make predictions based on the data. For example, a normal distribution is characterized by its mean and standard deviation, while a Poisson distribution models the number of events occurring within a fixed interval of time or space. Understanding statistical distributions is crucial for interpreting medical research findings and making informed decisions in healthcare.

Statistical models are mathematical representations that describe the relationship between variables in a given dataset. They are used to analyze and interpret data in order to make predictions or test hypotheses about a population. In the context of medicine, statistical models can be used for various purposes such as:

1. Disease risk prediction: By analyzing demographic, clinical, and genetic data using statistical models, researchers can identify factors that contribute to an individual's risk of developing certain diseases. This information can then be used to develop personalized prevention strategies or early detection methods.

2. Clinical trial design and analysis: Statistical models are essential tools for designing and analyzing clinical trials. They help determine sample size, allocate participants to treatment groups, and assess the effectiveness and safety of interventions.

3. Epidemiological studies: Researchers use statistical models to investigate the distribution and determinants of health-related events in populations. This includes studying patterns of disease transmission, evaluating public health interventions, and estimating the burden of diseases.

4. Health services research: Statistical models are employed to analyze healthcare utilization, costs, and outcomes. This helps inform decisions about resource allocation, policy development, and quality improvement initiatives.

5. Biostatistics and bioinformatics: In these fields, statistical models are used to analyze large-scale molecular data (e.g., genomics, proteomics) to understand biological processes and identify potential therapeutic targets.

In summary, statistical models in medicine provide a framework for understanding complex relationships between variables and making informed decisions based on data-driven insights.

Biometry, also known as biometrics, is the scientific study of measurements and statistical analysis of living organisms. In a medical context, biometry is often used to refer to the measurement and analysis of physical characteristics or features of the human body, such as height, weight, blood pressure, heart rate, and other physiological variables. These measurements can be used for a variety of purposes, including diagnosis, treatment planning, monitoring disease progression, and research.

In addition to physical measurements, biometry may also refer to the use of statistical methods to analyze biological data, such as genetic information or medical images. This type of analysis can help researchers and clinicians identify patterns and trends in large datasets, and make predictions about health outcomes or treatment responses.

Overall, biometry is an important tool in modern medicine, as it allows healthcare professionals to make more informed decisions based on data and evidence.

Statistical data interpretation involves analyzing and interpreting numerical data in order to identify trends, patterns, and relationships. This process often involves the use of statistical methods and tools to organize, summarize, and draw conclusions from the data. The goal is to extract meaningful insights that can inform decision-making, hypothesis testing, or further research.

In medical contexts, statistical data interpretation is used to analyze and make sense of large sets of clinical data, such as patient outcomes, treatment effectiveness, or disease prevalence. This information can help healthcare professionals and researchers better understand the relationships between various factors that impact health outcomes, develop more effective treatments, and identify areas for further study.

Some common statistical methods used in data interpretation include descriptive statistics (e.g., mean, median, mode), inferential statistics (e.g., hypothesis testing, confidence intervals), and regression analysis (e.g., linear, logistic). These methods can help medical professionals identify patterns and trends in the data, assess the significance of their findings, and make evidence-based recommendations for patient care or public health policy.

Binomial distribution is a type of discrete probability distribution that describes the number of successes in a fixed number of independent Bernoulli trials with the same probability of success. It is called a "binomial" distribution because it involves the sum of two outcomes: success and failure. The binomial distribution is defined by two parameters: n, the number of trials, and p, the probability of success on any given trial. The possible values of the random variable range from 0 to n.

The formula for calculating the probability mass function (PMF) of a binomial distribution is:

P(X=k) = C(n, k) \* p^k \* (1-p)^(n-k),

where X is the number of successes, n is the number of trials, k is the specific number of successes, p is the probability of success on any given trial, and C(n, k) is the number of combinations of n items taken k at a time.

Binomial distribution has many applications in medical research, such as testing the effectiveness of a treatment or diagnostic test, where the trials could represent individual patients or samples, and success could be defined as a positive response to treatment or a correct diagnosis.

Reference values, also known as reference ranges or reference intervals, are the set of values that are considered normal or typical for a particular population or group of people. These values are often used in laboratory tests to help interpret test results and determine whether a patient's value falls within the expected range.

The process of establishing reference values typically involves measuring a particular biomarker or parameter in a large, healthy population and then calculating the mean and standard deviation of the measurements. Based on these statistics, a range is established that includes a certain percentage of the population (often 95%) and excludes extreme outliers.

It's important to note that reference values can vary depending on factors such as age, sex, race, and other demographic characteristics. Therefore, it's essential to use reference values that are specific to the relevant population when interpreting laboratory test results. Additionally, reference values may change over time due to advances in measurement technology or changes in the population being studied.

A computer simulation is a process that involves creating a model of a real-world system or phenomenon on a computer and then using that model to run experiments and make predictions about how the system will behave under different conditions. In the medical field, computer simulations are used for a variety of purposes, including:

1. Training and education: Computer simulations can be used to create realistic virtual environments where medical students and professionals can practice their skills and learn new procedures without risk to actual patients. For example, surgeons may use simulation software to practice complex surgical techniques before performing them on real patients.
2. Research and development: Computer simulations can help medical researchers study the behavior of biological systems at a level of detail that would be difficult or impossible to achieve through experimental methods alone. By creating detailed models of cells, tissues, organs, or even entire organisms, researchers can use simulation software to explore how these systems function and how they respond to different stimuli.
3. Drug discovery and development: Computer simulations are an essential tool in modern drug discovery and development. By modeling the behavior of drugs at a molecular level, researchers can predict how they will interact with their targets in the body and identify potential side effects or toxicities. This information can help guide the design of new drugs and reduce the need for expensive and time-consuming clinical trials.
4. Personalized medicine: Computer simulations can be used to create personalized models of individual patients based on their unique genetic, physiological, and environmental characteristics. These models can then be used to predict how a patient will respond to different treatments and identify the most effective therapy for their specific condition.

Overall, computer simulations are a powerful tool in modern medicine, enabling researchers and clinicians to study complex systems and make predictions about how they will behave under a wide range of conditions. By providing insights into the behavior of biological systems at a level of detail that would be difficult or impossible to achieve through experimental methods alone, computer simulations are helping to advance our understanding of human health and disease.

Bayes' theorem, also known as Bayes' rule or Bayes' formula, is a fundamental principle in the field of statistics and probability theory. It describes how to update the probability of a hypothesis based on new evidence or data. The theorem is named after Reverend Thomas Bayes, who first formulated it in the 18th century.

In mathematical terms, Bayes' theorem states that the posterior probability of a hypothesis (H) given some observed evidence (E) is proportional to the product of the prior probability of the hypothesis (P(H)) and the likelihood of observing the evidence given the hypothesis (P(E|H)):

Posterior Probability = P(H|E) = [P(E|H) x P(H)] / P(E)

Where:

* P(H|E): The posterior probability of the hypothesis H after observing evidence E. This is the probability we want to calculate.
* P(E|H): The likelihood of observing evidence E given that the hypothesis H is true.
* P(H): The prior probability of the hypothesis H before observing any evidence.
* P(E): The marginal likelihood or probability of observing evidence E, regardless of whether the hypothesis H is true or not. This value can be calculated as the sum of the products of the likelihood and prior probability for all possible hypotheses: P(E) = Σ[P(E|Hi) x P(Hi)]

Bayes' theorem has many applications in various fields, including medicine, where it can be used to update the probability of a disease diagnosis based on test results or other clinical findings. It is also widely used in machine learning and artificial intelligence algorithms for probabilistic reasoning and decision making under uncertainty.

Statistics, as a topic in the context of medicine and healthcare, refers to the scientific discipline that involves the collection, analysis, interpretation, and presentation of numerical data or quantifiable data in a meaningful and organized manner. It employs mathematical theories and models to draw conclusions, make predictions, and support evidence-based decision-making in various areas of medical research and practice.

Some key concepts and methods in medical statistics include:

1. Descriptive Statistics: Summarizing and visualizing data through measures of central tendency (mean, median, mode) and dispersion (range, variance, standard deviation).
2. Inferential Statistics: Drawing conclusions about a population based on a sample using hypothesis testing, confidence intervals, and statistical modeling.
3. Probability Theory: Quantifying the likelihood of events or outcomes in medical scenarios, such as diagnostic tests' sensitivity and specificity.
4. Study Designs: Planning and implementing various research study designs, including randomized controlled trials (RCTs), cohort studies, case-control studies, and cross-sectional surveys.
5. Sampling Methods: Selecting a representative sample from a population to ensure the validity and generalizability of research findings.
6. Multivariate Analysis: Examining the relationships between multiple variables simultaneously using techniques like regression analysis, factor analysis, or cluster analysis.
7. Survival Analysis: Analyzing time-to-event data, such as survival rates in clinical trials or disease progression.
8. Meta-Analysis: Systematically synthesizing and summarizing the results of multiple studies to provide a comprehensive understanding of a research question.
9. Biostatistics: A subfield of statistics that focuses on applying statistical methods to biological data, including medical research.
10. Epidemiology: The study of disease patterns in populations, which often relies on statistical methods for data analysis and interpretation.

Medical statistics is essential for evidence-based medicine, clinical decision-making, public health policy, and healthcare management. It helps researchers and practitioners evaluate the effectiveness and safety of medical interventions, assess risk factors and outcomes associated with diseases or treatments, and monitor trends in population health.

An algorithm is not a medical term, but rather a concept from computer science and mathematics. In the context of medicine, algorithms are often used to describe step-by-step procedures for diagnosing or managing medical conditions. These procedures typically involve a series of rules or decision points that help healthcare professionals make informed decisions about patient care.

For example, an algorithm for diagnosing a particular type of heart disease might involve taking a patient's medical history, performing a physical exam, ordering certain diagnostic tests, and interpreting the results in a specific way. By following this algorithm, healthcare professionals can ensure that they are using a consistent and evidence-based approach to making a diagnosis.

Algorithms can also be used to guide treatment decisions. For instance, an algorithm for managing diabetes might involve setting target blood sugar levels, recommending certain medications or lifestyle changes based on the patient's individual needs, and monitoring the patient's response to treatment over time.

Overall, algorithms are valuable tools in medicine because they help standardize clinical decision-making and ensure that patients receive high-quality care based on the latest scientific evidence.

Genetic models are theoretical frameworks used in genetics to describe and explain the inheritance patterns and genetic architecture of traits, diseases, or phenomena. These models are based on mathematical equations and statistical methods that incorporate information about gene frequencies, modes of inheritance, and the effects of environmental factors. They can be used to predict the probability of certain genetic outcomes, to understand the genetic basis of complex traits, and to inform medical management and treatment decisions.

There are several types of genetic models, including:

1. Mendelian models: These models describe the inheritance patterns of simple genetic traits that follow Mendel's laws of segregation and independent assortment. Examples include autosomal dominant, autosomal recessive, and X-linked inheritance.
2. Complex trait models: These models describe the inheritance patterns of complex traits that are influenced by multiple genes and environmental factors. Examples include heart disease, diabetes, and cancer.
3. Population genetics models: These models describe the distribution and frequency of genetic variants within populations over time. They can be used to study evolutionary processes, such as natural selection and genetic drift.
4. Quantitative genetics models: These models describe the relationship between genetic variation and phenotypic variation in continuous traits, such as height or IQ. They can be used to estimate heritability and to identify quantitative trait loci (QTLs) that contribute to trait variation.
5. Statistical genetics models: These models use statistical methods to analyze genetic data and infer the presence of genetic associations or linkage. They can be used to identify genetic risk factors for diseases or traits.

Overall, genetic models are essential tools in genetics research and medical genetics, as they allow researchers to make predictions about genetic outcomes, test hypotheses about the genetic basis of traits and diseases, and develop strategies for prevention, diagnosis, and treatment.

I'm sorry for any confusion, but the "Monte Carlo method" is actually a term from the field of mathematics and computer science, not medicine. It refers to a statistical technique that allows for the modeling of complex systems by running multiple simulations with random inputs. This method is widely used in various fields such as physics, engineering, and finance, but it is not a medical concept or term.

A quantitative trait is a phenotypic characteristic that can be measured and displays continuous variation, meaning it can take on any value within a range. Examples include height, blood pressure, or biochemical measurements like cholesterol levels. These traits are usually influenced by the combined effects of multiple genes (polygenic inheritance) as well as environmental factors.

Heritability, in the context of genetics, refers to the proportion of variation in a trait that can be attributed to genetic differences among individuals in a population. It is estimated using statistical methods and ranges from 0 to 1, with higher values indicating a greater contribution of genetics to the observed phenotypic variance.

Therefore, a heritable quantitative trait would be a phenotype that shows continuous variation, influenced by multiple genes and environmental factors, and for which a significant portion of the observed variation can be attributed to genetic differences among individuals in a population.

In the context of medicine and healthcare, 'probability' does not have a specific medical definition. However, in general terms, probability is a branch of mathematics that deals with the study of numerical quantities called probabilities, which are assigned to events or sets of events. Probability is a measure of the likelihood that an event will occur. It is usually expressed as a number between 0 and 1, where 0 indicates that the event is impossible and 1 indicates that the event is certain to occur.

In medical research and statistics, probability is often used to quantify the uncertainty associated with statistical estimates or hypotheses. For example, a p-value is a probability that measures the strength of evidence against a hypothesis. A small p-value (typically less than 0.05) suggests that the observed data are unlikely under the assumption of the null hypothesis, and therefore provides evidence in favor of an alternative hypothesis.

Probability theory is also used to model complex systems and processes in medicine, such as disease transmission dynamics or the effectiveness of medical interventions. By quantifying the uncertainty associated with these models, researchers can make more informed decisions about healthcare policies and practices.

Reproducibility of results in a medical context refers to the ability to obtain consistent and comparable findings when a particular experiment or study is repeated, either by the same researcher or by different researchers, following the same experimental protocol. It is an essential principle in scientific research that helps to ensure the validity and reliability of research findings.

In medical research, reproducibility of results is crucial for establishing the effectiveness and safety of new treatments, interventions, or diagnostic tools. It involves conducting well-designed studies with adequate sample sizes, appropriate statistical analyses, and transparent reporting of methods and findings to allow other researchers to replicate the study and confirm or refute the results.

The lack of reproducibility in medical research has become a significant concern in recent years, as several high-profile studies have failed to produce consistent findings when replicated by other researchers. This has led to increased scrutiny of research practices and a call for greater transparency, rigor, and standardization in the conduct and reporting of medical research.

Quantitative Trait Loci (QTL) are regions of the genome that are associated with variation in quantitative traits, which are traits that vary continuously in a population and are influenced by multiple genes and environmental factors. QTLs can help to explain how genetic variations contribute to differences in complex traits such as height, blood pressure, or disease susceptibility.

Quantitative trait loci are identified through statistical analysis of genetic markers and trait values in experimental crosses between genetically distinct individuals, such as strains of mice or plants. The location of a QTL is inferred based on the pattern of linkage disequilibrium between genetic markers and the trait of interest. Once a QTL has been identified, further analysis can be conducted to identify the specific gene or genes responsible for the variation in the trait.

It's important to note that QTLs are not themselves genes, but rather genomic regions that contain one or more genes that contribute to the variation in a quantitative trait. Additionally, because QTLs are identified through statistical analysis, they represent probabilistic estimates of the location of genetic factors influencing a trait and may encompass large genomic regions containing multiple genes. Therefore, additional research is often required to fine-map and identify the specific genes responsible for the variation in the trait.

"Likelihood functions" is a statistical concept that is used in medical research and other fields to estimate the probability of obtaining a given set of data, given a set of assumptions or parameters. In other words, it is a function that describes how likely it is to observe a particular outcome or result, based on a set of model parameters.

More formally, if we have a statistical model that depends on a set of parameters θ, and we observe some data x, then the likelihood function is defined as:

L(θ | x) = P(x | θ)

This means that the likelihood function describes the probability of observing the data x, given a particular value of the parameter vector θ. By convention, the likelihood function is often expressed as a function of the parameters, rather than the data, so we might instead write:

L(θ) = P(x | θ)

The likelihood function can be used to estimate the values of the model parameters that are most consistent with the observed data. This is typically done by finding the value of θ that maximizes the likelihood function, which is known as the maximum likelihood estimator (MLE). The MLE has many desirable statistical properties, including consistency, efficiency, and asymptotic normality.

In medical research, likelihood functions are often used in the context of Bayesian analysis, where they are combined with prior distributions over the model parameters to obtain posterior distributions that reflect both the observed data and prior knowledge or assumptions about the parameter values. This approach is particularly useful when there is uncertainty or ambiguity about the true value of the parameters, as it allows researchers to incorporate this uncertainty into their analyses in a principled way.

In clinical research, sample size refers to the number of participants or observations included in a study. It is a critical aspect of study design that can impact the validity and generalizability of research findings. A larger sample size typically provides more statistical power, which means that it is more likely to detect true effects if they exist. However, increasing the sample size also increases the cost and time required for a study. Therefore, determining an appropriate sample size involves balancing statistical power with practical considerations.

The calculation of sample size depends on several factors, including the expected effect size, the variability of the outcome measure, the desired level of statistical significance, and the desired power of the study. Statistical software programs are often used to calculate sample sizes that balance these factors while minimizing the overall sample size required to detect a meaningful effect.

It is important to note that a larger sample size does not necessarily mean that a study is more rigorous or well-designed. The quality of the study's methods, including the selection of participants, the measurement of outcomes, and the analysis of data, are also critical factors that can impact the validity and generalizability of research findings.

In medical terms, "breeding" is not a term that is commonly used. It is more frequently used in the context of animal husbandry to refer to the process of mating animals in order to produce offspring with specific desired traits or characteristics. In human medicine, the term is not typically applied to people and instead, related concepts such as reproduction, conception, or pregnancy are used.

I'm sorry for any confusion, but "Markov Chains" is a term from the field of mathematics and probability theory, not medicine. Markov Chains are mathematical systems that undergo transitions from one state to another according to certain probabilistic rules. They are named after Russian mathematician Andrey Markov. These chains are used in various fields, including computer science, physics, economics, and engineering, but not commonly in medical definitions or contexts.

Biological models, also known as physiological models or organismal models, are simplified representations of biological systems, processes, or mechanisms that are used to understand and explain the underlying principles and relationships. These models can be theoretical (conceptual or mathematical) or physical (such as anatomical models, cell cultures, or animal models). They are widely used in biomedical research to study various phenomena, including disease pathophysiology, drug action, and therapeutic interventions.

Examples of biological models include:

1. Mathematical models: These use mathematical equations and formulas to describe complex biological systems or processes, such as population dynamics, metabolic pathways, or gene regulation networks. They can help predict the behavior of these systems under different conditions and test hypotheses about their underlying mechanisms.
2. Cell cultures: These are collections of cells grown in a controlled environment, typically in a laboratory dish or flask. They can be used to study cellular processes, such as signal transduction, gene expression, or metabolism, and to test the effects of drugs or other treatments on these processes.
3. Animal models: These are living organisms, usually vertebrates like mice, rats, or non-human primates, that are used to study various aspects of human biology and disease. They can provide valuable insights into the pathophysiology of diseases, the mechanisms of drug action, and the safety and efficacy of new therapies.
4. Anatomical models: These are physical representations of biological structures or systems, such as plastic models of organs or tissues, that can be used for educational purposes or to plan surgical procedures. They can also serve as a basis for developing more sophisticated models, such as computer simulations or 3D-printed replicas.

Overall, biological models play a crucial role in advancing our understanding of biology and medicine, helping to identify new targets for therapeutic intervention, develop novel drugs and treatments, and improve human health.

I'm sorry for any confusion, but "Linear Models" is actually a term from the field of statistics and machine learning, rather than medicine. A linear model is a type of statistical model that is used to analyze the relationship between two or more variables. In a linear model, the relationship between the dependent variable (the outcome or result) and the independent variable(s) (the factors being studied) is assumed to be linear, meaning that it can be described by a straight line on a graph.

The equation for a simple linear model with one independent variable (x) and one dependent variable (y) looks like this:

y = β0 + β1*x + ε

In this equation, β0 is the y-intercept or the value of y when x equals zero, β1 is the slope or the change in y for each unit increase in x, and ε is the error term or the difference between the actual values of y and the predicted values of y based on the linear model.

Linear models are widely used in medical research to study the relationship between various factors (such as exposure to a risk factor or treatment) and health outcomes (such as disease incidence or mortality). They can also be used to adjust for confounding variables, which are factors that may influence both the independent variable and the dependent variable, and thus affect the observed relationship between them.

A phenotype is the physical or biochemical expression of an organism's genes, or the observable traits and characteristics resulting from the interaction of its genetic constitution (genotype) with environmental factors. These characteristics can include appearance, development, behavior, and resistance to disease, among others. Phenotypes can vary widely, even among individuals with identical genotypes, due to differences in environmental influences, gene expression, and genetic interactions.

Analysis of Variance (ANOVA) is a statistical technique used to compare the means of two or more groups and determine whether there are any significant differences between them. It is a way to analyze the variance in a dataset to determine whether the variability between groups is greater than the variability within groups, which can indicate that the groups are significantly different from one another.

ANOVA is based on the concept of partitioning the total variance in a dataset into two components: variance due to differences between group means (also known as "between-group variance") and variance due to differences within each group (also known as "within-group variance"). By comparing these two sources of variance, ANOVA can help researchers determine whether any observed differences between groups are statistically significant, or whether they could have occurred by chance.

ANOVA is a widely used technique in many areas of research, including biology, psychology, engineering, and business. It is often used to compare the means of two or more experimental groups, such as a treatment group and a control group, to determine whether the treatment had a significant effect. ANOVA can also be used to compare the means of different populations or subgroups within a population, to identify any differences that may exist between them.

Genetic variation refers to the differences in DNA sequences among individuals and populations. These variations can result from mutations, genetic recombination, or gene flow between populations. Genetic variation is essential for evolution by providing the raw material upon which natural selection acts. It can occur within a single gene, between different genes, or at larger scales, such as differences in the number of chromosomes or entire sets of chromosomes. The study of genetic variation is crucial in understanding the genetic basis of diseases and traits, as well as the evolutionary history and relationships among species.

Genetic markers are specific segments of DNA that are used in genetic mapping and genotyping to identify specific genetic locations, diseases, or traits. They can be composed of short tandem repeats (STRs), single nucleotide polymorphisms (SNPs), restriction fragment length polymorphisms (RFLPs), or variable number tandem repeats (VNTRs). These markers are useful in various fields such as genetic research, medical diagnostics, forensic science, and breeding programs. They can help to track inheritance patterns, identify genetic predispositions to diseases, and solve crimes by linking biological evidence to suspects or victims.

In the field of medicine, "time factors" refer to the duration of symptoms or time elapsed since the onset of a medical condition, which can have significant implications for diagnosis and treatment. Understanding time factors is crucial in determining the progression of a disease, evaluating the effectiveness of treatments, and making critical decisions regarding patient care.

For example, in stroke management, "time is brain," meaning that rapid intervention within a specific time frame (usually within 4.5 hours) is essential to administering tissue plasminogen activator (tPA), a clot-busting drug that can minimize brain damage and improve patient outcomes. Similarly, in trauma care, the "golden hour" concept emphasizes the importance of providing definitive care within the first 60 minutes after injury to increase survival rates and reduce morbidity.

Time factors also play a role in monitoring the progression of chronic conditions like diabetes or heart disease, where regular follow-ups and assessments help determine appropriate treatment adjustments and prevent complications. In infectious diseases, time factors are crucial for initiating antibiotic therapy and identifying potential outbreaks to control their spread.

Overall, "time factors" encompass the significance of recognizing and acting promptly in various medical scenarios to optimize patient outcomes and provide effective care.

Pregnancy is a physiological state or condition where a fertilized egg (zygote) successfully implants and grows in the uterus of a woman, leading to the development of an embryo and finally a fetus. This process typically spans approximately 40 weeks, divided into three trimesters, and culminates in childbirth. Throughout this period, numerous hormonal and physical changes occur to support the growing offspring, including uterine enlargement, breast development, and various maternal adaptations to ensure the fetus's optimal growth and well-being.

"Cattle" is a term used in the agricultural and veterinary fields to refer to domesticated animals of the genus *Bos*, primarily *Bos taurus* (European cattle) and *Bos indicus* (Zebu). These animals are often raised for meat, milk, leather, and labor. They are also known as bovines or cows (for females), bulls (intact males), and steers/bullocks (castrated males). However, in a strict medical definition, "cattle" does not apply to humans or other animals.

The term "Theoretical Models" is used in various scientific fields, including medicine, to describe a representation of a complex system or phenomenon. It is a simplified framework that explains how different components of the system interact with each other and how they contribute to the overall behavior of the system. Theoretical models are often used in medical research to understand and predict the outcomes of diseases, treatments, or public health interventions.

A theoretical model can take many forms, such as mathematical equations, computer simulations, or conceptual diagrams. It is based on a set of assumptions and hypotheses about the underlying mechanisms that drive the system. By manipulating these variables and observing the effects on the model's output, researchers can test their assumptions and generate new insights into the system's behavior.

Theoretical models are useful for medical research because they allow scientists to explore complex systems in a controlled and systematic way. They can help identify key drivers of disease or treatment outcomes, inform the design of clinical trials, and guide the development of new interventions. However, it is important to recognize that theoretical models are simplifications of reality and may not capture all the nuances and complexities of real-world systems. Therefore, they should be used in conjunction with other forms of evidence, such as experimental data and observational studies, to inform medical decision-making.

Sensitivity and specificity are statistical measures used to describe the performance of a diagnostic test or screening tool in identifying true positive and true negative results.

* Sensitivity refers to the proportion of people who have a particular condition (true positives) who are correctly identified by the test. It is also known as the "true positive rate" or "recall." A highly sensitive test will identify most or all of the people with the condition, but may also produce more false positives.
* Specificity refers to the proportion of people who do not have a particular condition (true negatives) who are correctly identified by the test. It is also known as the "true negative rate." A highly specific test will identify most or all of the people without the condition, but may also produce more false negatives.

In medical testing, both sensitivity and specificity are important considerations when evaluating a diagnostic test. High sensitivity is desirable for screening tests that aim to identify as many cases of a condition as possible, while high specificity is desirable for confirmatory tests that aim to rule out the condition in people who do not have it.

It's worth noting that sensitivity and specificity are often influenced by factors such as the prevalence of the condition in the population being tested, the threshold used to define a positive result, and the reliability and validity of the test itself. Therefore, it's important to consider these factors when interpreting the results of a diagnostic test.

Oligonucleotide Array Sequence Analysis is a type of microarray analysis that allows for the simultaneous measurement of the expression levels of thousands of genes in a single sample. In this technique, oligonucleotides (short DNA sequences) are attached to a solid support, such as a glass slide, in a specific pattern. These oligonucleotides are designed to be complementary to specific target mRNA sequences from the sample being analyzed.

During the analysis, labeled RNA or cDNA from the sample is hybridized to the oligonucleotide array. The level of hybridization is then measured and used to determine the relative abundance of each target sequence in the sample. This information can be used to identify differences in gene expression between samples, which can help researchers understand the underlying biological processes involved in various diseases or developmental stages.

It's important to note that this technique requires specialized equipment and bioinformatics tools for data analysis, as well as careful experimental design and validation to ensure accurate and reproducible results.

"Age factors" refer to the effects, changes, or differences that age can have on various aspects of health, disease, and medical care. These factors can encompass a wide range of issues, including:

1. Physiological changes: As people age, their bodies undergo numerous physical changes that can affect how they respond to medications, illnesses, and medical procedures. For example, older adults may be more sensitive to certain drugs or have weaker immune systems, making them more susceptible to infections.
2. Chronic conditions: Age is a significant risk factor for many chronic diseases, such as heart disease, diabetes, cancer, and arthritis. As a result, age-related medical issues are common and can impact treatment decisions and outcomes.
3. Cognitive decline: Aging can also lead to cognitive changes, including memory loss and decreased decision-making abilities. These changes can affect a person's ability to understand and comply with medical instructions, leading to potential complications in their care.
4. Functional limitations: Older adults may experience physical limitations that impact their mobility, strength, and balance, increasing the risk of falls and other injuries. These limitations can also make it more challenging for them to perform daily activities, such as bathing, dressing, or cooking.
5. Social determinants: Age-related factors, such as social isolation, poverty, and lack of access to transportation, can impact a person's ability to obtain necessary medical care and affect their overall health outcomes.

Understanding age factors is critical for healthcare providers to deliver high-quality, patient-centered care that addresses the unique needs and challenges of older adults. By taking these factors into account, healthcare providers can develop personalized treatment plans that consider a person's age, physical condition, cognitive abilities, and social circumstances.

Electron microscopy (EM) is a type of microscopy that uses a beam of electrons to create an image of the sample being examined, resulting in much higher magnification and resolution than light microscopy. There are several types of electron microscopy, including transmission electron microscopy (TEM), scanning electron microscopy (SEM), and reflection electron microscopy (REM).

In TEM, a beam of electrons is transmitted through a thin slice of the sample, and the electrons that pass through the sample are focused to form an image. This technique can provide detailed information about the internal structure of cells, viruses, and other biological specimens, as well as the composition and structure of materials at the atomic level.

In SEM, a beam of electrons is scanned across the surface of the sample, and the electrons that are scattered back from the surface are detected to create an image. This technique can provide information about the topography and composition of surfaces, as well as the structure of materials at the microscopic level.

REM is a variation of SEM in which the beam of electrons is reflected off the surface of the sample, rather than scattered back from it. This technique can provide information about the surface chemistry and composition of materials.

Electron microscopy has a wide range of applications in biology, medicine, and materials science, including the study of cellular structure and function, disease diagnosis, and the development of new materials and technologies.

Regression analysis is a statistical technique used in medicine, as well as in other fields, to examine the relationship between one or more independent variables (predictors) and a dependent variable (outcome). It allows for the estimation of the average change in the outcome variable associated with a one-unit change in an independent variable, while controlling for the effects of other independent variables. This technique is often used to identify risk factors for diseases or to evaluate the effectiveness of medical interventions. In medical research, regression analysis can be used to adjust for potential confounding variables and to quantify the relationship between exposures and health outcomes. It can also be used in predictive modeling to estimate the probability of a particular outcome based on multiple predictors.

Multivariate analysis is a statistical method used to examine the relationship between multiple independent variables and a dependent variable. It allows for the simultaneous examination of the effects of two or more independent variables on an outcome, while controlling for the effects of other variables in the model. This technique can be used to identify patterns, associations, and interactions among multiple variables, and is commonly used in medical research to understand complex health outcomes and disease processes. Examples of multivariate analysis methods include multiple regression, factor analysis, cluster analysis, and discriminant analysis.

Gene expression profiling is a laboratory technique used to measure the activity (expression) of thousands of genes at once. This technique allows researchers and clinicians to identify which genes are turned on or off in a particular cell, tissue, or organism under specific conditions, such as during health, disease, development, or in response to various treatments.

The process typically involves isolating RNA from the cells or tissues of interest, converting it into complementary DNA (cDNA), and then using microarray or high-throughput sequencing technologies to determine which genes are expressed and at what levels. The resulting data can be used to identify patterns of gene expression that are associated with specific biological states or processes, providing valuable insights into the underlying molecular mechanisms of diseases and potential targets for therapeutic intervention.

In recent years, gene expression profiling has become an essential tool in various fields, including cancer research, drug discovery, and personalized medicine, where it is used to identify biomarkers of disease, predict patient outcomes, and guide treatment decisions.

A mutation is a permanent change in the DNA sequence of an organism's genome. Mutations can occur spontaneously or be caused by environmental factors such as exposure to radiation, chemicals, or viruses. They may have various effects on the organism, ranging from benign to harmful, depending on where they occur and whether they alter the function of essential proteins. In some cases, mutations can increase an individual's susceptibility to certain diseases or disorders, while in others, they may confer a survival advantage. Mutations are the driving force behind evolution, as they introduce new genetic variability into populations, which can then be acted upon by natural selection.

"Cells, cultured" is a medical term that refers to cells that have been removed from an organism and grown in controlled laboratory conditions outside of the body. This process is called cell culture and it allows scientists to study cells in a more controlled and accessible environment than they would have inside the body. Cultured cells can be derived from a variety of sources, including tissues, organs, or fluids from humans, animals, or cell lines that have been previously established in the laboratory.

Cell culture involves several steps, including isolation of the cells from the tissue, purification and characterization of the cells, and maintenance of the cells in appropriate growth conditions. The cells are typically grown in specialized media that contain nutrients, growth factors, and other components necessary for their survival and proliferation. Cultured cells can be used for a variety of purposes, including basic research, drug development and testing, and production of biological products such as vaccines and gene therapies.

It is important to note that cultured cells may behave differently than they do in the body, and results obtained from cell culture studies may not always translate directly to human physiology or disease. Therefore, it is essential to validate findings from cell culture experiments using additional models and ultimately in clinical trials involving human subjects.

The simplest case of a normal distribution is known as the standard normal distribution or unit normal distribution. This is a ... The normal distribution is a subclass of the elliptical distributions. The normal distribution is symmetric about its mean, and ... and Distributions modeled as normal - the normal distribution being the distribution with maximum entropy for a given mean and ... Measurement errors in physical experiments are often modeled by a normal distribution. This use of a normal distribution does ...
... the skew normal distribution is a continuous probability distribution that generalises the normal distribution to allow for non ... skew multivariate t distribution and others. The distribution is a particular case of a general class of distributions with ... Then the probability density function (pdf) of the skew-normal distribution with parameter α {\displaystyle \alpha } is given ... A stochastic process that underpins the distribution was described by Andel, Netuka and Zvara (1984). Both the distribution and ...
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Wikimedia Commons has media related to Log-normal distribution. The normal distribution is the log-normal distribution ( ... Continuous distributions, Normal distribution, Exponential family distributions, Infinitely divisible probability distributions ... The distribution of higher-income individuals follows a Pareto distribution). If an income distribution follows a log-normal ... Equivalently, if Y has a normal distribution, then the exponential function of Y, X = exp(Y), has a log-normal distribution. A ...
The split normal distribution results from merging two halves of normal distributions. In a general case the 'parent' normal ... In probability theory and statistics, the split normal distribution also known as the two-piece normal distribution results ... of normal distributions in their common mode. The PDF of the split normal distribution is given by f ( x ; μ , σ 1 , σ 2 ) = A ... the split normal distribution reduces to normal distribution with variance σ ∗ 2 {\displaystyle \sigma _{*}^{2}} . When σ2≠σ1 ...
Half-t distribution Truncated normal distribution Folded normal distribution Rectified Gaussian distribution Gelman, A. (2006 ... follows a half-normal distribution. Thus, the half-normal distribution is a fold at the mean of an ordinary normal distribution ... see truncated normal distribution) If Y has a half-normal distribution, then (Y/σ)2 has a chi square distribution with 1 degree ... In probability theory and statistics, the half-normal distribution is a special case of the folded normal distribution. Let X ...
Multivariate normal distribution A K Gupta; D K Nagar (22 October 1999). "Chapter 2: MATRIX VARIATE NORMAL DISTRIBUTION". ... In statistics, the matrix normal distribution or matrix Gaussian distribution is a probability distribution that is a ... Dawid (1981) provides a discussion of the relation of the matrix-valued normal distribution to other distributions, including ... from the matrix normal distribution is a special case of the sampling procedure for the multivariate normal distribution. Let X ...
The Student-t distribution, the Irwin-Hall distribution and the Bates distribution also extend the normal distribution, and ... Complex normal distribution Skew normal distribution Griffin, Maryclare. "Working with the Exponential Power Distribution Using ... The t distribution, unlike this generalized normal distribution, obtains heavier than normal tails without acquiring a cusp at ... For example, the log-normal, folded normal, and inverse normal distributions are defined as transformations of a normally- ...
... a logit-normal distribution is a probability distribution of a random variable whose logit has a normal distribution. If Y is a ... the distribution is bimodal. The logistic normal distribution is a generalization of the logit-normal distribution to D- ... The logistic normal distribution is a more flexible alternative to the Dirichlet distribution in that it can capture ... is the inverse cumulative distribution function of a normal distribution with mean and variance μ , σ 2 {\textstyle \mu ,\sigma ...
The folded normal distribution is a probability distribution related to the normal distribution. Given a normally distributed ... Folded cumulative distribution Half-normal distribution Modified half-normal distribution with the pdf on ( 0 , ∞ ) {\ ... The Rice distribution is a multivariate generalization of the folded normal distribution. Modified half-normal distribution ... the distribution of Y is a half-normal distribution. The random variable (Y/σ)2 has a noncentral chi-squared distribution with ...
The normal distributions transform (NDT) is a point cloud registration algorithm introduced by Peter Biber and Wolfgang Straßer ... The algorithm registers two point clouds by first associating a piecewise normal distribution to the first point cloud, that ... 10-11, 13) Biber, Peter; Straßer, Wolfgang (2003). "The normal distributions transform: A new approach to laser scan matching ... Magnusson, Martin (2009). The three-dimensional normal-distributions transform: an efficient representation for registration, ...
Multivariate continuous distributions, Conjugate prior distributions, Normal distribution). ... Here λ, α and β are parameters of the joint distribution. Then (X,T) has a normal-gamma distribution, and this is denoted by ( ... In probability theory and statistics, the normal-gamma distribution (or Gaussian-gamma distribution) is a bivariate four- ... The normal-inverse-gamma distribution is essentially the same distribution parameterized by variance rather than precision The ...
... a wrapped normal distribution is a wrapped probability distribution that results from the "wrapping" of the normal distribution ... the circular moments of the wrapped normal distribution are the characteristic function of the normal distribution evaluated at ... e iθn drawn from a wrapped normal distribution may be used to estimate certain parameters of the distribution. The average of ... which is a useful measure of dispersion for the wrapped normal distribution and its close relative, the von Mises distribution ...
The multivariate normal distribution and Wishart distribution are the component distributions out of which this distribution is ... Multivariate continuous distributions, Conjugate prior distributions, Normal distribution). ... In probability theory and statistics, the normal-Wishart distribution (or Gaussian-Wishart distribution) is a multivariate four ... is a multivariate normal distribution. The marginal distribution over μ {\displaystyle {\boldsymbol {\mu }}} is a multivariate ...
Normal distribution Multivariate normal distribution (a complex normal distribution is a bivariate normal distribution) ... Complex normal ratio distribution Directional statistics § Distribution of the mean (polar form) ... Continuous distributions, Multivariate continuous distributions, Complex distributions, Articles with math errors, Articles ... In probability theory, the family of complex normal distributions, denoted C N {\displaystyle {\mathcal {CN}}} or N C {\ ...
... the projected normal distribution (also known as offset normal distribution or angular normal distribution) is a probability ... the distribution is symmetric. The density of the projected normal distribution P N n ( μ , Σ ) {\displaystyle {\mathcal {PN ... are the density and cumulative distribution of a standard normal distribution, T ( θ ) = v ⊤ Σ − 1 μ v ⊤ Σ − 1 v {\displaystyle ... Directional statistics Multivariate normal distribution Wang & Gelfand 2013. Hernandez-Stumpfhauser & Breidt 2017, p. 115. sfn ...
... the multivariate normal distribution, multivariate Gaussian distribution, or joint normal distribution is a generalization of ... both have a normal distribution does not imply that the pair ( X , Y ) {\displaystyle (X,Y)} has a joint normal distribution. A ... has a univariate normal distribution, where a univariate normal distribution with zero variance is a point mass on its mean. ... The direction of a normal vector follows a projected normal distribution. If f ( x ) {\displaystyle f({\boldsymbol {x}})} is a ...
See the articles on normal-gamma distribution and conjugate prior. See the articles on normal-gamma distribution and conjugate ... The normal-inverse-Wishart distribution is a generalization of the normal-inverse-gamma distribution that is defined over ... In probability theory and statistics, the normal-inverse-gamma distribution (or Gaussian-inverse-gamma distribution) is a four- ... The normal-gamma distribution is the same distribution parameterized by precision rather than variance A generalization of this ...
As for the Laplace distribution, the pdf of the NEG distribution can be expressed as a mixture of normal distributions, f ( x ... In probability theory and statistics, the normal-exponential-gamma distribution (sometimes called the NEG distribution) is a ... of the normal-exponential-gamma distribution is proportional to f ( x ; μ , k , θ ) ∝ exp ⁡ ( ( x − μ ) 2 4 θ 2 ) D − 2 k − 1 ... the distribution-names should be interpreted as meaning the density functions of those distributions. Within this scale mixture ...
The multivariate normal distribution and inverse Wishart distribution are the component distributions out of which this ... Multivariate continuous distributions, Conjugate prior distributions, Normal distribution). ... In probability theory and statistics, the normal-inverse-Wishart distribution (or Gaussian-inverse-Wishart distribution) is a ... The normal-Wishart distribution is essentially the same distribution parameterized by precision rather than variance. If ( μ , ...
The normal-inverse Gaussian distribution (NIG, also known as the normal-Wald distribution) is a continuous probability ... The normal-inverse Gaussian distribution can also be seen as the marginal distribution of the normal-inverse Gaussian process ... Hyperbolic Distributions and Distributions on Hyperbolae, Scandinavian Journal of Statistics 1978 O. Barndorff-Nielsen, Normal ... The class of normal-inverse Gaussian distributions is closed under convolution in the following sense: if X 1 {\displaystyle X ...
The truncated normal distribution, half-normal distribution, and square root of the gamma distribution are special cases of the ... The modified half normal distribution is an exponential family of distributions. Therefore, the properties of the exponential ... The name of the distribution is motivated by the similarities of its density function with that of the half-normal distribution ... the family of modified half-normal distributions (MHN) is a three-parameter family of continuous probability distributions ...
Tong, Y. L. (2 July 2020). "Multivariate normal distribution". Wikipedia. Misra, Rishabh (7 June 2020). "Inference using EM ... See Categorical distribution. The following procedure can be used to estimate ϕ , μ , Σ {\displaystyle \phi ,\mu ,\Sigma } . A ...
matrix gamma distribution. matrix normal distribution. matrix t-distribution. Wishart distribution. Iranmanesha, Anis; Arashib ... as the conjugate prior of the covariance matrix of a multivariate normal distribution or matrix normal distribution. The ... In statistics, the inverse matrix gamma distribution is a generalization of the inverse gamma distribution to positive-definite ... M.; Tabatabaeya, S. M. M. (2010). "On Conditional Applications of Matrix Variate Normal Distribution". Iranian Journal of ...
Binomial Distribution; Poisson Distributions; Continuous Probability Distributions; The Normal Distribution; Estimation; ... The coverage of "Further Statistics" includes: Continuous Probability Distributions; Estimation; Hypothesis Testing; One Sample ... "variability is normal" and how "coincidences… are not uncommon because there are so many possibilities." Gal (2002) suggests ... approach of reasoning under the null and the restrictions of normal theory, they use comparative box plots and bootstrap to ...
... inverse matrix gamma distribution. matrix normal distribution. matrix t-distribution. Wishart distribution. Iranmanesh, Anis, M ... as the conjugate prior of the precision matrix of a multivariate normal distribution and matrix normal distribution. The ... In statistics, a matrix gamma distribution is a generalization of the gamma distribution to positive-definite matrices. It is a ... Arashib and S. M. M. Tabatabaey (2010). "On Conditional Applications of Matrix Variate Normal Distribution". Iranian Journal of ...
Occasionally, heavy-tailed is used for any distribution that has heavier tails than the normal distribution.) The distribution ... Those that are one-tailed include: the Pareto distribution; the Log-normal distribution; the Lévy distribution; the Weibull ... The t-distribution. The skew lognormal cascade distribution. A fat-tailed distribution is a distribution for which the ... the log-logistic distribution; the log-gamma distribution; the Fréchet distribution; the q-Gaussian distribution the log-Cauchy ...
The normal distribution has the highest entropy of any distribution for a given standard deviation. There are a number of ... The empirical distribution of the data (the histogram) should be bell-shaped and resemble the normal distribution. This might ... measures how well the data are modeled by a normal distribution. For normal data the points plotted in the QQ plot should fall ... of the standardized data against the standard normal distribution. Here the correlation between the sample data and normal ...
"Don't Risk Using Normal Distribution?". Financial Times. Anderson, Robert M.; Bianchi, Stephen W.; Goldberg, Lisa R. (November- ...
... variate normal distributions with unknown mean vectors μ i {\displaystyle \mu _{i}} and unknown dispersion matrices Σ i {\ ... the distribution of the T 2 {\displaystyle T^{2}} statistic is known to be an F distribution under the null and a noncentral F- ... The distributions of X i ¯ {\displaystyle {\bar {X_{i}}}} and A i {\displaystyle A_{i}} are independent and are, respectively, ... The test statistic T 2 {\displaystyle T^{2}} in Krishnmoorthy and Yu's procedure follows the distribution T 2 ∼ ν p F p , ν − p ...
... ❳ Previous Next ❳ The normal distribution is an important probability distribution used in ... Stat Statistical Inference Stat Normal Distribution Stat Standard Normal Distribution Stat Students T-Distribution Stat ... Normal Distribution. The normal distribution is described by the mean (\(\mu\)) and the standard deviation (\(\sigma\)). ... The mean describes where the center of the normal distribution is.. Here is a graph showing three different normal ...
The simplest case of a normal distribution is known as the standard normal distribution or unit normal distribution. This is a ... The normal distribution is a subclass of the elliptical distributions. The normal distribution is symmetric about its mean, and ... and Distributions modeled as normal - the normal distribution being the distribution with maximum entropy for a given mean and ... Measurement errors in physical experiments are often modeled by a normal distribution. This use of a normal distribution does ...
boost/random/normal_distribution.hpp. /* boost random/normal_distribution.hpp header file * * Copyright Jens Maurer 2000-2001 ... c normal_distribution to a @c std::ostream. */ BOOST_RANDOM_DETAIL_OSTREAM_OPERATOR(os, normal_distribution, nd) { os ,, nd._ ... c normal_distribution object from its parameters. */ explicit normal_distribution(const param_type& parm) : _mean(parm.mean ... normal_distribution; } // namespace boost #endif // BOOST_RANDOM_NORMAL_DISTRIBUTION_HPP ...
Finally, it is shown that the size (with suitable standardization) approaches the standard normal random variable in the ... The limiting distribution of the size of binary interval tree is investigated. Our illustration is based on the contraction ... has the same distribution as . Obviously, we can rewrite the above formula as. Define It is easy to see that ... are standard normal random variables, is uniformly distributed over interval , and are mutually independent and then one has. ...
The Normal Distribution is a continuous probability distribution defined by the mean and standard. ... The Normal Distribution is represented by your actual values. The Standard Normal Distribution is a form of Normal Distribution ... Wrapping up the Normal Distribution. The Normal Distribution is a continuous probability distribution defined by the mean and ... Overview: What is the Normal Distribution?. The Normal Distribution, also known as the Gaussian Distribution, is a hypothetical ...
A distribution of values that cluster around an average (referred to as the "mean") is known as a "normal" distribution. It is ... function returns a normal distribution of random numbers with the following parameters: a mean of zero and a standard deviation ... If we want to produce a random number with a normal (or Gaussian) distribution each time we run through draw(). , its as easy ... Luckily for us, to use a normal distribution of random numbers in a program here, we dont have to do any of these calculations ...
Normal Distribution. 163537 Solving a Normal Distribution Problem What are the characteristics of the normal distribution? Why ... Standard Normal Distribution Define a standard normal distribution. Why does a researcher want to go from a normal distribution ... 169626 The Normal Curve of Distribution: Definition, Shape, Formula How would you define the normal curve of distribution? Why ... c) State that neither the normal nor the t distribution applies. //cf for previous problem 21722.Normal distribution does not ...
... distributions that are non-normal the sampling distribution of , , , Xbar is , , , approximately normal for sufficiently large ... Re: st: Re: normal distributions. From. Scott Merryman ,[email protected],. To. ,[email protected],. Subject ... Re: st: Re: normal distributions. Date. Sun, 21 Jul 2002 13:58:17 -0600. You can also demonstrate the central limit theorem in ... RE: st: Re: normal distributions *From: Gene Fisher ,[email protected], ...
... Vahid Borji v@h,d@borj,65 @end,ng ,rom gm@,,@com Wed Jun 17 17:35:24 CEST ... Next message (by thread): [R] mnormt package for bivariate normal distribution * Messages sorted by: [ date ] [ thread ] [ ... Next message (by thread): [R] mnormt package for bivariate normal distribution * Messages sorted by: [ date ] [ thread ] [ ... Hi, my R friends, I am going to plot the surface of a bivariate normal distribution and its contours. I have written the below ...
The distribution of this molecule in normal and pathological synovia from patients with osteoarthritis (OA) and rheumatoid ... Tenascin and fibronectin distribution in human normal and pathological synovium J Rheumatol. 1992 Sep;19(9):1439-47. ... The distribution of this molecule in normal and pathological synovia from patients with osteoarthritis (OA) and rheumatoid ... However, a higher density and spreading pattern of distribution was observed in OA and RA sections. A-Fn and B-Fn isoforms were ...
Code to compute the inverse of the normal (Gaussian) distribution ... Since the standard normal distribution is symmetric about zero ... complementary cumulative distribution function) for a standard normal. Also, A&S says that the approximation is good for 0 , p ... Let F(x) be the CDF of a standard normal and let G(x) be the corresponding CCDF. We want to compute the inverse CDF, F-1(p), ... A literate program to compute the inverse of the normal CDF. This page presents C++ code for computing the inverse of the ...
Suggested for: How to prove the normal distribution tail inequality for large x ? A Discrete type normal distribution ... How can we use the above two formulas of CDF of Normal distribution to prove lemma 7.1 in the original question?. I got the ... In the above expansions of CDF of standard normal distribution, I want to know how the highlighted or marked computations was ... MHB Likelihood Ratio Test for Common Variance from Two Normal Distribution Samples ...
Alternatively, one might want random numbers from some other distribution such as a standard normal distribution. ... Tag: normal distribution. Generate random numbers in MS Excel. Posted on July 7, 2013. by Tushar Mehta ... For example, to generate a random number from a standard normal distribution, use =NORM.S.INV(RAND()) ... normal distribution, random number, uniform distribution 5 Comments ...
... normal_distribution); ax.set_ylim(0); ax.set_title(Normal Distribution, size = 20); ax.set_ylabel(Probability Density, size ... The normal distribution is commonly associated with the 68-95-99.7 rule. which you can see in the image above. 68% of the data ... but this is very rare if you have a normal or nearly normal distribution. ... Explaining the 68-95-99.7 rule for a Normal Distribution. This post explains how those numbers were derived in the hope that ...
Great resource for improving my class fluency with the normal distribution. Empty reply does not make any sense for the end ...
... The Normal (or Gaussian) Distribution is the most common probability distribution function (PDF) and is ... Truncated Normal Distribution. A truncated Normal Distribution can be defined for a variable by setting the desired minimum and ... For a Normal Distribution, about 68% of observations should fall within one standard deviation of the mean, and about 95% of ... and maximum values that are at least three standard deviations away from the mean generate a complete normal distribution. If ...
... distributions can result in an apparently symmetric or asymmetric unimodal distribution or a clearly bimodal distribution ... depending on the means standard deviations and weight fractions of the component distributions.; ... The Bivariate Normal Distribution. Chris Boucher. *. Impact of Sample Size on Approximating the Normal Distribution. Paul ... The Log Normal Distribution. Chris Boucher. *. Intuitive Parameterization of the Bivariate Normal Distribution. Robert L. Brown ...
The Normal Distribution, Part Two: Shoplifting (1031). This film builds on the Normal distribution, introduced in film 11, by ... DeSTRESS Film 12: The Normal Distribution, Part Two. Home » Educational materials » By subject » Statistics for social sciences ...
Truncated normal distribution using gsl_rng_gaussian, chadia kanaan, 2008/12/22. *Re: [Help-gsl] Truncated normal distribution ... RE: [Help-gsl] Truncated normal distribution using gsl_rng_gaussian. From: Abbas Alhakim. ... RE: [Help-gsl] Truncated normal distribution using gsl_rng_gaussian, Abbas Alhakim ,= ... Next by Date: Re: Fw : [Help-gsl] Truncated normal distribution using gsl_rng_gaussian ...
Power Log Normal Distribution#. A generalization of the log-normal distribution with shape parameters \(\sigma,0\), \(c,0\) and ...
Remarks on Algorithm 226: Normal distribution function. By S. J. Cyvin Communications of the ACM, June 1967, Vol. 10 No. 6, ...
... the impacts of the choice of climate normals is rarely considered. Here, we produced species distribution models for five ... climate normals time periods. Although the correlation structure among climate predictors did not change between the time ... Species distribution models have many applications in conservation and ecology, and climate data are frequently a key driver of ... Not so normal normals: Species distribution model results are sensitive to choice of climate normals and model type. Climate ...
Calculating A Normal Cumulative Distribution (normalcdf) on the TI-Nspire™ Family Handhelds ... How do I calculate a Normal Cumulative Distribution (normal cdf) using the TI-Nspire Handheld? How do I calculate a Normal ... Solution 36294: Calculating A Normal Cumulative Distribution (normalcdf) on the TI-Nspire™ Family Handhelds ... normal cdf) using the TI-Npsire Handheld? Use the following example as a guide when calculating for the normal CDF with a TI- ...
... There are various components which come into play in decision making. Though not the only ... www.ukessays.com/essays/statistics/applying-the-normal-distribution.php?vref=1 ,title=Applying the Normal Distribution , ... According to Fox, Levin, and Forde (2013), the example of a grade curve is known as the normal distribution or normal curve. ... There is also the "Empirical Rule" of a normal distribution is relating to the areas beneath or under the normal curve; (1) ...
Performance Comparison for Effort Estimation Models with Log-Normal and Gamma Distributions S. Amasaki (Japan) ... As a result, it was found that log-normal and Gamma regressions have contrasting characteristics though the difference is ... Furthermore, it was found that which error distribution is favored depends on what one wants to estimate. These results ... This study compared log-normal and Gamma regressions for effort estimation in terms of their predictive performance. Both ...
This improved version of the BMTME model was derived using the matrix normal distribution that allows a more easy derivation of ... all full conditional distributions required, allows a more efficient model in terms of time of implementation. We tested the ... Matrix normal distribution. The matrix normal distribution is a probability distribution that is a generalization of the ... with a normal matrix distribution b. 2 ∼ MN. IJ. × L. (. 0. , Σ. E. ⊗ G. g. , Σ. t. ) and e. is of order n. × L. with a normal ...
mean", and click on "COMPARE CURVES" to see the normal curves. The top curve is generated using the SD inputted, and the bottom ... Then, once you click on the "CALCULATE" button, see the result, graph and normal curves by clicking on "RESULT", "GRAPH" and " ... Then, click on the "CALCULATE" button AGAIN, to obtain the result, graph, and normal curves, as in (A). ... Retrieved from "http://wiki.stat.ucla.edu/socr/index.php/Power_Analysis_for_Normal_Distribution:" ...
Probability on a Normal Distribution: Two values, different sides. by Megan Rehm on Aug 12, 2017. ...
Age- and gender-related changes in the distribution of osteocalcin in the extracellular matrix of normal male and female bone. ... Four different distribution patterns of osteocalcin within individual osteons were arbitrarily defined as types I, II, III, or ... These results suggest that differences in the distribution of osteocalcin in bone matrix may be responsible, in part, for the ... Whether age- and/or gender-related differences exist in the distribution of osteocalcin within individual bone remodeling units ...
... we will learn how to use the normal distribution to calculate probabilities and find unknown variables and parameters. ... understand and use the shape and symmetry of the normal distribution as well as key facts relating to the mean and standard ... use normal distribution tables to find probabilities that correspond to a specific 𝑧. -scores, ... In this lesson, we will learn how to use the normal distribution to calculate probabilities and find unknown variables and ...
  • In statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. (wikipedia.org)
  • A random variable with a Gaussian distribution is said to be normally distributed, and is called a normal deviate. (wikipedia.org)
  • Moreover, Gaussian distributions have some unique properties that are valuable in analytic studies. (wikipedia.org)
  • This variate is also called the standardized form of X {\displaystyle X} . The probability density of the standard Gaussian distribution (standard normal distribution, with zero mean and unit variance) is often denoted with the Greek letter ϕ {\displaystyle \phi } (phi). (wikipedia.org)
  • The Normal Distribution, also known as the Gaussian Distribution, is a hypothetical mathematical construct and one of the most common statistical distributions. (isixsigma.com)
  • It is also called the Gaussian distribution (named for mathematician Carl Friedrich Gauss) or, if you are French, the Laplacian distribution (named for Pierre-Simon Laplace). (khanacademy.org)
  • This page presents C++ code for computing the inverse of the normal (Gaussian) CDF. (johndcook.com)
  • x ) = p where Z is a standard normal (Gaussian) random variable. (johndcook.com)
  • The Normal (or Gaussian) Distribution is the most common probability distribution function (PDF) and is generally used for probabilistic studies in geotechnical engineering. (rocscience.com)
  • In this article, we have to create an array of specified shape and fill it random numbers or values such that these values are part of a normal distribution or Gaussian distribution. (geeksforgeeks.org)
  • The normal, or Gaussian, distribution has a density function that is a symmetrical bell-shaped curve. (stackexchange.com)
  • I have been reading Pattern Recognition and Machine Learning by Bishop, and I have a question regarding the prior distribution of an iid Gaussian with known variance. (stackexchange.com)
  • In some cases, you can use the Normal Distribution to approximate discrete distributions such as the Binomial and Poisson . (isixsigma.com)
  • Using the normal curve approximation to the binomial distribution , find the probability of 265 heads or more. (brainmass.com)
  • A normal distribution is sometimes informally called a bell curve. (wikipedia.org)
  • There various way to describe the statistics, including a normal curve, bell curve, central limit theorem, and z-scores which will be discussed below. (ukessays.com)
  • Why is the bell curve used to represent the normal distribution and not a different shape? (ukessays.com)
  • This distribution is also called the Bell Curve this is because of its characteristics shape. (geeksforgeeks.org)
  • How to Create a Normal Distribution Graph (Bell Curve) in Excel? (educba.com)
  • The Empirical Rule describes how the individual values of your data would be distributed under the distribution curve if your data was normally distributed. (isixsigma.com)
  • For a normally distributed population, the sampling distribution is also normal when there are sufficient test items in the samples . (explorable.com)
  • However, many other distributions are bell-shaped (such as the Cauchy, Student's t, and logistic distributions). (wikipedia.org)
  • The normal distribution is an important probability distribution used in statistics. (w3schools.com)
  • It is one of the most important probability distributions in statistics because it accurately describes the distribution of values for many natural phenomena. (isixsigma.com)
  • In 1809, Johann Carl Friedrich Gauss, a German mathematician and physicist described the distribution in the context of measurement errors in astronomy. (isixsigma.com)
  • The univariate probability distribution is generalized for vectors in the multivariate normal distribution and for matrices in the matrix normal distribution. (wikipedia.org)
  • Among other tests evaluated, this study suggested the use of the Elliptical Test with Least Squares (Elliptical Theory), Heterogeneous Kurtosis Test with Reweighted Least Squares (Heterogeneous Kurtosis Theory) and Satorra-Bentler Scaled Test with Maximum Likelihood estimation (for distributions with excessive univariate asymmetry and/or kurtosis). (bvsalud.org)
  • Based on this definition, a copula is a "multivariate probability distribution for which the marginal probability distribution of each variable is uniform. (r-bloggers.com)
  • Since we can generate a multivariate normal \(\mathbf{X}\) , it is relatively short leap to implement this copula algorithm in order to generate correlated data from other distributions. (r-bloggers.com)
  • In a simulated and exploratory approach, distinct distributions were analyzed in terms of multivariate kurtosis. (bvsalud.org)
  • Such a distribution produces random numbers * @c x distributed with probability density function * \f$\displaystyle p(x) = * \frac{1}{\sqrt{2\pi}\sigma} e^{-\frac{(x-\mu)^2}{2\sigma^2}} * \f$, * where mean and sigma are the parameters of the distribution. (boost.org)
  • The Normal Distribution is described by only two parameters, the mean and standard deviation making calculations easy to do. (isixsigma.com)
  • In this lesson, we will learn how to use the normal distribution to calculate probabilities and find unknown variables and parameters. (nagwa.com)
  • The parameters allow you to specify the length of the dataseries to be generated, the mean of the distribution, and the standard error of the distribution. (wessa.net)
  • The area under the curve of the normal distribution represents probabilities for the data. (w3schools.com)
  • Since the Normal Distribution is a hypothetical curve there is no such thing as a Normal Distribution in the real world. (isixsigma.com)
  • Definition, Shape, Formula How would you define the normal curve of distribution ? (brainmass.com)
  • Why do you think the normal curve of distribution is a bell shape? (brainmass.com)
  • According to Fox, Levin, and Forde (2013), the example of a grade curve is known as the normal distribution or normal curve. (ukessays.com)
  • There are specific characteristics of a normal curve such as "a smooth, symmetrical distribution that is bell-shapes and unimodal" (Fox, Levin, & Forde, 2013, p. 88). (ukessays.com)
  • A normal curve has the mean, median, and mode in the same position, in the middle or center of the curve which is symmetric as "each side is a mirror image of the other" (Weiers, 2011, p. 208). (ukessays.com)
  • According to Fox, Levin, and Forde (2013), a normal curve is unimodal as it only has one peak or point of maximum likelihood in the middle of the curve. (ukessays.com)
  • Thus a normal distribution will result in a normal curve in a bell-shaped curve. (ukessays.com)
  • According to Weiers (2011), the shape of a normal curve will depend on its mean and standard deviation, though maintain a variation of a bell-shaped curve. (ukessays.com)
  • Note that in (B)'s normal curve, the data are ploted in pink (based on frequency). (ucla.edu)
  • A normal distribution graph in Excel, plotted as a bell-shaped curve, shows the chances of a specific event or value. (educba.com)
  • What is a Normal Distribution Curve? (educba.com)
  • The normal distribution is a bell-shaped curve often appearing in various phenomena around us. (educba.com)
  • We need software to compute the inverse of the normal CDF (cumulative density function). (johndcook.com)
  • While there are specialized algorithms to generate random numbers from specific distributions, a common approach relies on generating uniform random numbers and then using the inverse function of the desired distribution. (dailydoseofexcel.com)
  • In the next step, there is always a discussion of variables which are non-normal and potential "cures" like sqrt, log, inverse etc. (stackexchange.com)
  • Since we can write the gamma intervals as a simple function of the inverse chi-squared distribution, they are practical to use in any situation. (cdc.gov)
  • I recently reread some statistics books and noted something weird: They all discuss the assumptions of linear regression and mention the need for a normal distributed dependent variable. (stackexchange.com)
  • Variational Bayesian Inference is a popular methodology for approximating posterior distributions over Bayesian neural network weights. (mlr.press)
  • Attenuation of the PDR can also be seen as a low-voltage normal variant, in this case the other principles underpinning a normal background are present including reactivity, variability, and anterior to posterior gradient with faster frequencies anterior. (medscape.com)
  • We refer to these new confidence intervals as gamma intervals, since the approximation is based on the gamma distribution. (cdc.gov)
  • You can use a graphical Probability Plot or a statistical test like the Anderson-Darling test and use the p-value to test whether your data is non-normal. (isixsigma.com)
  • As one of the most common statistical distributions, there are a number of benefits of the Normal Distribution. (isixsigma.com)
  • The Normal Distribution can be used to model many common processes and as such, is the underlying assumption for the use of many statistical tools. (isixsigma.com)
  • This allows you to use inferential statistical methods that assume normality, even if the individual data in your sample doesn't follow a Normal Distribution. (isixsigma.com)
  • Why is the normal distribution important in statistical analysis? (brainmass.com)
  • Then you could click on the "RESULT" button to see the statistical output, and click on "GRAPH" tab to see a plot of "power vs. mean", and click on "COMPARE CURVES" to see the normal curves. (ucla.edu)
  • The statistical estimation problem of the normal distribution function and of the density at a point is considered. (impan.pl)
  • If the error distribution is not normal and the assumption of normality is made, then there could lead to an incorrect statistical analysis and thus erroneous conclusions. (explorable.com)
  • There are statistical tests that a researcher can undertake which help determine whether the normal distribution assumptions are valid or not. (explorable.com)
  • The normal distribution excel function, NORMDIST , is a statistical function that helps to get a probability of values according to a mean value. (educba.com)
  • This improved version of the BMTME model was derived using the matrix normal distribution that allows a more easy derivation of all full conditional distributions required, allows a more efficient model in terms of time of implementation. (intechopen.com)
  • It states that, under some conditions, the average of many samples (observations) of a random variable with finite mean and variance is itself a random variable-whose distribution converges to a normal distribution as the number of samples increases. (wikipedia.org)
  • Probabilities of the normal distribution can only be calculated for intervals (between two values). (w3schools.com)
  • Probability distributions are functions that calculates the probabilities of the outcomes of random variables. (w3schools.com)
  • This solution shows how to find probabilities of events from a known normal probability distribution. (brainmass.com)
  • The graph above shows us the distribution with a very low standard deviation, where the majority of the values cluster closely around the mean. (khanacademy.org)
  • Then, once you click on the "CALCULATE" button, see the result, graph and normal curves by clicking on "RESULT", "GRAPH" and "COMPARE CURVES" tabs. (ucla.edu)
  • We can plot normal distribution Excel graph to see if each student is getting more, less, or proper sleep compared to the average sleep. (educba.com)
  • The above mathematical formula for the normal distribution graph may look complex, so Excel has added this in-built Excel function to simplify it. (educba.com)
  • A school teacher, William, wants to find the normal distribution graph for his students' marks. (educba.com)
  • The M sets of imputations for the missing values are ideally independent draws from the predictive distribution of the missing values conditional on the observed values. (cdc.gov)
  • The simplest case of a normal distribution is known as the standard normal distribution or unit normal distribution. (wikipedia.org)
  • As a result of being such a common distribution, statisticians have developed a number of Normal and Standard Normal Distribution tables which can be used for calculations and predictions. (isixsigma.com)
  • 469386 Statistics Problem for standard normal distribution 1. (brainmass.com)
  • 237533 Statistics - Standard Normal Distribution Define a standard normal distribution . (brainmass.com)
  • Why does a researcher want to go from a normal distribution to a standard normal distribution ? (brainmass.com)
  • Since the standard normal distribution is symmetric about zero, the probability of being greater than x is the same as the probability of being less than - x . (johndcook.com)
  • I got the following proofs of expansion of CDF of standard normal distribution. (physicsforums.com)
  • In the above expansions of CDF of standard normal distribution, I want to know how the highlighted or marked computations was performed. (physicsforums.com)
  • Alternatively, one might want random numbers from some other distribution such as a standard normal distribution. (dailydoseofexcel.com)
  • The general form of its probability density function is f ( x ) = 1 σ 2 π e − 1 2 ( x − μ σ ) 2 {\displaystyle f(x)={\frac {1}{\sigma {\sqrt {2\pi }}}}e^{-{\frac {1}{2}}\left({\frac {x-\mu }{\sigma }}\right)^{2}}} The parameter μ {\displaystyle \mu } is the mean or expectation of the distribution (and also its median and mode), while the parameter σ {\displaystyle \sigma } is its standard deviation. (wikipedia.org)
  • The formula for the Normal Distribution probability density function is shown below. (isixsigma.com)
  • This definition might not make much sense so let's clear it up by graphing the probability density function for a normal distribution. (kdnuggets.com)
  • Normal probability density function, showing standard deviation ranges. (rocscience.com)
  • Generate from the tail using rejection sampling from the exponential(x_1) distribution, // shifted by x_1. (boost.org)
  • For practical purposes, minimum and maximum values that are at least three standard deviations away from the mean generate a complete normal distribution. (rocscience.com)
  • package, it's possible to generate correlated data from a normal distribution using the function genCorData . (r-bloggers.com)
  • To generate five random numbers from the normal distribution we will use numpy.random.normal() method of the random module. (geeksforgeeks.org)
  • Greater torque for the elliptic cylinders was associated with 58% greater normal force that the subjects could generate for the elliptic than circular cylinders. (cdc.gov)
  • Age- and gender-related changes in the distribution of osteocalcin in the extracellular matrix of normal male and female bone. (jci.org)
  • In this study, we determined the immunohistochemical distribution of osteocalcin in the extracellular matrix of iliac crest bone biopsies obtained from normal male and female volunteers, 20-80 yr old. (jci.org)
  • The normal distribution drawn on top of the histogram is based on the population mean (\(\mu\)) and standard deviation (\(\sigma\)) of the real data. (w3schools.com)
  • This film builds on the Normal distribution, introduced in film 11 , by giving various examples, focusing on the losses from shoplifting in various shops. (economicsnetwork.ac.uk)
  • Therefore, physical quantities that are expected to be the sum of many independent processes, such as measurement errors, often have distributions that are nearly normal. (wikipedia.org)
  • For example, one might assume symmetry, as in a t-distribution even if the distribution is not truly normal. (explorable.com)
  • A major benefit of the normal distribution is the linkage to the Central Limit Theorem . (isixsigma.com)
  • How do I calculate a Normal Cumulative Distribution (normal cdf) using the TI-Nspire Handheld? (ti.com)
  • Cumulative" is a logical value where "true" or "false" decides how to calculate the normal distribution. (educba.com)
  • True" will calculate the normal distribution for all values less than or equal to your selected x-value. (educba.com)
  • How to Calculate Normal Distribution in Excel? (educba.com)
  • Let us now learn how to calculate a normal distribution for any data in Excel. (educba.com)
  • Although the density above is most commonly known as the standard normal, a few authors have used that term to describe other versions of the normal distribution. (wikipedia.org)
  • Despite its simplicity, there are some things to keep in mind when using the Normal Distribution to describe your process data. (isixsigma.com)
  • g) Describe the distribution of the sample means: What is its shape? (brainmass.com)
  • As with all probability distributions, the Normal Distribution describes how the values of your data are distributed. (isixsigma.com)
  • If your data is not approximately distributed as the above, you may not want to declare your data is normal. (isixsigma.com)
  • If less than .05, you will reject the null hypothesis and conclude the data is not normal. (isixsigma.com)
  • The Normal Distribution is only a good predictor if you have an adequate amount of data. (isixsigma.com)
  • It takes a sufficient amount of data for the distribution to form. (isixsigma.com)
  • The Normal Distribution is a continuous distribution so it is only valid for continuous data . (isixsigma.com)
  • Species distribution models have many applications in conservation and ecology, and climate data are frequently a key driver of these models. (usgs.gov)
  • This paper aims to evaluate techniques for correcting the chi-square test (X 2 ) as applied to Confirmatory Factor Analysis (CFA) models in non-normal data. (bvsalud.org)
  • The reason for the normal distribution assumptions is that this is usually the simplest mathematical model that can be used. (explorable.com)
  • This posting helps with a problem involving normal distribution and populations. (brainmass.com)
  • The solution examines normal distribution and populations using an ANOVA test. (brainmass.com)
  • This theorem states that when the sample size is sufficiently large, the distribution of sample means will approach a normal distribution regardless of the shape of the distribution from which the samples came from. (isixsigma.com)
  • approximately normal for sufficiently large samples. (stata.com)
  • The expected values of the coin toss is the probability distribution of the coin toss. (w3schools.com)
  • As we keep increasing the number of dice for a sum the shape of the results and expected values look more and more like a normal distribution. (w3schools.com)
  • This Demonstration shows how mixing two normal distributions can result in an apparently symmetric or asymmetric unimodal distribution or a clearly bimodal distribution, depending on the means, standard deviations, and weight fractions of the component distributions. (wolfram.com)
  • Normal distributions are important in statistics and are often used in the natural and social sciences to represent real-valued random variables whose distributions are not known. (wikipedia.org)
  • During the 19th century, this distribution was widely applied in the areas of applied probability and statistics. (isixsigma.com)
  • It is one of the most important distributions in statistics. (stackexchange.com)
  • namespace detail /** * Instantiations of class template normal_distribution model a * \random_distribution. (boost.org)
  • While these studies carefully determined predictor variables and model formulation, error distributions are fewer considered. (actapress.com)
  • Distributors who are considering or already pivoting toward the remote distribution model and virtual distribution have more than likely experienced an uncomfortable transition. (acumatica.com)
  • Another common requirement is the generation of integer random numbers from a uniform distribution. (dailydoseofexcel.com)
  • The measured earth pressures show that the airbag with stiff plates resulted in a nonuniform pressure distribution, whereas the tests with an airbag directly on the soil had an approximately uniform pressure distribution. (ku.edu)
  • Finally, it is shown that the size (with suitable standardization) approaches the standard normal random variable in the Zolotarev metric space. (hindawi.com)
  • Itoh and Mahmoud [ 13 ] considered five incomplete one-sided variants of binary interval trees and proved that their sizes all approach some normal random variables. (hindawi.com)
  • We usually assume that the random errors follow a normal distribution. (explorable.com)
  • This free online software (calculator) generates a specified number of random series for the Log-Normal distribution. (wessa.net)
  • Dobson, Kuulasmaa, Eberle and Scherer (hereafter DKES) introduced confidence limits for weighted sums of Poisson random variables that, unlike the traditional confidence limits based on the normal distribution (see Clayton and Hills), do not require large cell counts. (cdc.gov)
  • 163537 Solving a Normal Distribution Problem What are the characteristics of the normal distribution ? (brainmass.com)
  • As a result, it was found that log-normal and Gamma regressions have contrasting characteristics though the difference is diminished when uncertainty of effort is well explained by predictor variables. (actapress.com)
  • The normal background should have a number of defining characteristics. (medscape.com)
  • I would like to receive email from ImperialX and learn about other offerings related to A-level Mathematics for Year 13 - Course 2: General Motion, Moments and Equilibrium, The Normal Distribution, Vectors, Differentiation Methods, Integration Methods and Differential Equations. (edx.org)
  • Hi, my R friends, I am going to plot the surface of a bivariate normal distribution and its contours. (ethz.ch)
  • Consider the family of all continuous distributions with finite $r-th$ moment (where $r \geq 1$ is a given integer). (stackexchange.com)
  • Utilizing an eCommerce platform integrated with a cloud ERP solution, distributors can easily manage virtual distribution selling methods, such as dropshipments. (acumatica.com)
  • If the physical process can be approximated by a normal distribution, it will yield the simplest analysis. (explorable.com)
  • In the laboratory pullout test, the reinforcement is embedded in the soil mass at a normal stress, which is commonly applied by a pressurized airbag or a hydraulic jack through a rigid plate, and then a horizontal tensile force is applied to the reinforcement. (ku.edu)
  • There is the asymptotic tail which signifies the less than or almost zero of the normal distribution and "approaches the x-axis but never reaches it" (Weiers, 2011, p. 208). (ukessays.com)
  • The demonstration of immunoreactive IFN-alpha in formalin fixed paraffin embedded normal adult human tissues prompted other studies. (gla.ac.uk)
  • In the first of these studies the cellular distribution of immunoreactive IFN-alpha was studied in formalin fixed paraffin embedded normal human autopsy tissues from 32 fetuses (7-42 weeks gestation) and 20 infants (aged from a few hours to 24 months). (gla.ac.uk)
  • Fetal tissues are "germ free" while the infants had been exposed to a normal microbial flora. (gla.ac.uk)
  • Finally an attempt was made to detect IFN-alpha messenger RNA (mRNA) in normal human tissues using an in situ hybridization method. (gla.ac.uk)
  • Normal Distribution = This is going to be the most common type. (benefitresource.com)
  • Each HSA distribution type has a specific purpose and, specific tax treatment considerations. (benefitresource.com)