Poisson Distribution
Binomial Distribution
Models, Statistical
Mathematics
Models, Theoretical
Incidence
Models, Genetic
Computer Simulation
Algorithms
Asthma visits to emergency rooms and soybean unloading in the harbors of Valencia and A Coruna, Spain. (1/1869)
Soybean unloading in the harbor of Barcelona, Spain, has been associated with large increases in the numbers of asthma patients treated in emergency departments between 1981 and 1987. In this study, the association between asthma and soybean unloading in two other Spanish cities, Valencia and A Coruna, was assessed. Asthma admissions were retrospectively identified for the period 1993-1995, and harbor activities were investigated in each location. Two approaches were used to assess the association between asthma and soybean unloading: One used unusual asthma days (days with an unusually high number of emergency room asthma visits) as an effect measure, and the other estimated the relative increase in the daily number of emergency room visits by autoregressive Poisson regression, adjusted for meteorologic variables, seasonality, and influenza incidence. No association between unusual asthma days and soya unloading was observed in either Valencia or A Coruna, except for one particular dock in Valencia. When the association between unloaded products and the daily number of emergency asthma visits was studied, a statistically significant association was observed for unloading of soya husk (relative risk = 1.50, 95% confidence interval 1.16-1.94) and soybeans (relative risk = 1.31, 95% confidence interval 1.08-1.59) in A Coruna. In Valencia, a statistical association was found only for the unloading of soybeans at two particular docks. Although these findings support the notion that asthma outbreaks are not a common hidden condition in most harbors where soybeans are unloaded, the weak associations reported are likely to be causal. Therefore, appropriate control measures should be implemented to avoid soybean dust emissions, particularly in harbors with populations living in the vicinity. (+info)Testing the fit of a quantal model of neurotransmission. (2/1869)
Many studies of synaptic transmission have assumed a parametric model to estimate the mean quantal content and size or the effect upon them of manipulations such as the induction of long-term potentiation. Classical tests of fit usually assume that model parameters have been selected independently of the data. Therefore, their use is problematic after parameters have been estimated. We hypothesized that Monte Carlo (MC) simulations of a quantal model could provide a table of parameter-independent critical values with which to test the fit after parameter estimation, emulating Lilliefors's tests. However, when we tested this hypothesis within a conventional quantal model, the empirical distributions of two conventional goodness-of-fit statistics were affected by the values of the quantal parameters, falsifying the hypothesis. Notably, the tests' critical values increased when the combined variances of the noise and quantal-size distributions were reduced, increasing the distinctness of quantal peaks. Our results support two conclusions. First, tests that use a predetermined critical value to assess the fit of a quantal model after parameter estimation may operate at a differing unknown level of significance for each experiment. Second, a MC test enables a valid assessment of the fit of a quantal model after parameter estimation. (+info)Air pollution, pollens, and daily admissions for asthma in London 1987-92. (3/1869)
BACKGROUND: A study was undertaken to investigate the relationship between daily hospital admissions for asthma and air pollution in London in 1987-92 and the possible confounding and modifying effects of airborne pollen. METHODS: For all ages together and the age groups 0-14, 15-64 and 65+ years, Poisson regression was used to estimate the relative risk of daily asthma admissions associated with changes in ozone, sulphur dioxide, nitrogen dioxide and particles (black smoke), controlling for time trends, seasonal factors, calendar effects, influenza epidemics, temperature, humidity, and autocorrelation. Independent effects of individual pollutants and interactions with aeroallergens were explored using two pollutant models and models including pollen counts (grass, oak and birch). RESULTS: In all-year analyses ozone was significantly associated with admissions in the 15-64 age group (10 ppb eight hour ozone, 3.93% increase), nitrogen dioxide in the 0-14 and 65+ age groups (10 ppb 24 hour nitrogen dioxide, 1.25% and 2.96%, respectively), sulphur dioxide in the 0-14 age group (10 micrograms/m3 24 hour sulphur dioxide, 1.64%), and black smoke in the 65% age group (10 micrograms/m3 black smoke, 5.60%). Significant seasonal differences were observed for ozone in the 0-14 and 15-64 age groups, and in the 0-14 age group there were negative associations with ozone in the cool season. In general, cumulative lags of up to three days tended to show stronger and more significant effects than single day lags. In two-pollutant models these associations were most robust for ozone and least for nitrogen dioxide. There was no evidence that the associations with air pollutants were due to confounding by any of the pollens, and little evidence of an interaction between pollens and pollution except for synergism of sulphur dioxide and grass pollen in children (p < 0.01). CONCLUSIONS: Ozone, sulphur dioxide, nitrogen dioxide, and particles were all found to have significant associations with daily hospital admissions for asthma, but there was a lack of consistency across the age groups in the specific pollutant. These associations were not explained by confounding by airborne pollens nor was there convincing evidence that the effects of air pollutants and airborne pollens interact in causing hospital admissions for asthma. (+info)Inequalities in mortality according to educational level in two large Southern European cities. (4/1869)
BACKGROUND: In Spain, studies on social inequalities in mortality based on individuals are few due to the poor quality of information on occupation in death certificates. This study looks at the differences in mortality according to educational level, using individual information obtained through the linkage between the Death Register and the Municipal Census, in the cities of Madrid and Barcelona, Spain. METHODS: The study populations were residents of Madrid and Barcelona aged >24 years, who died in 1993 and 1994. Indicators obtained for each city and educational level were: age- and sex-specific mortality rates, and life expectancy at 25 years. Poisson regression models were fitted to obtain the relative risk (RR) of death for each educational level with respect to the reference level (higher education completed), adjusted for age. RESULTS: The mortality rate was lower among individuals with higher educational levels, while life expectancy at 25 years was higher. In both cities men and women with no education showed the highest mortality in all age groups, with very high RR in the youngest age group (RR for men aged 25-34 years = 7.08 in Madrid and 6.02 in Barcelona, whereas in women these RR were 6.33 and 5.63 respectively). In Barcelona the greater part of the overall mortality difference for the group aged 25-34 years was due to AIDS (acquired deficiency syndrome, 33.4% in men and 59.3% in women). CONCLUSION: The present study has found higher mortality (mainly from AIDS) among individuals with no academic qualifications thus drawing attention to the need to implement policies aimed at reducing these inequalities. (+info)Health service accessibility and deaths from asthma. (5/1869)
BACKGROUND: Good access to health services may be important for effective asthma management amongst patients, thus preventing unnecessary deaths. In a previous study, we found elevated levels of asthma mortality in English local authority districts with poor access to acute hospitals. Here, the relationship between asthma mortality and access to primary and secondary services within the rural region of East Anglia is examined. METHODS: A geographically based descriptive study, within 536 electoral wards in the region of East Anglia, England. Regression analysis was used to examine the relationship between health service accessibility, and mortality from asthma during the period January 1985 to December 1995. RESULTS: After controlling for confounding factors, there was a significant tendency for asthma mortality to increase with travel time to hospital, with a relative risk of 1.07 for each 10-minute increase in journey time (P = 0.04). There was no consistent trend for mortality to increase with travel time to general practitioner surgeries. CONCLUSIONS: The results of this study support the conclusions of earlier work that inaccessibility of acute hospital services may increase the risk of asthma mortality. The provision of good access to these facilities may be one factor in reducing the burden of avoidable deaths from asthma. (+info)Early age at smoking initiation and tobacco carcinogen DNA damage in the lung. (6/1869)
BACKGROUND: DNA adducts formed as a consequence of exposure to tobacco smoke may be involved in carcinogenesis, and their presence may indicate a high risk of lung cancer. To determine whether DNA adducts can be used as a "dosimeter" for cancer risk, we measured the adduct levels in nontumorous lung tissue and blood mononuclear cells from patients with lung cancer, and we collected data from the patients on their history of smoking. METHODS: We used the 32P-postlabeling assay to measure aromatic hydrophobic DNA adducts in nontumorous lung tissue from 143 patients and in blood mononuclear cells from 54 of these patients. From the smoking histories, we identified exposure variables associated with increased DNA adduct levels by use of multivariate analyses with negative binomial regression models. RESULTS/ CONCLUSIONS: We found statistically significant interactions for variables of current and former smoking and for other smoking variables (e.g., pack-years [number of packs smoked per day x years of smoking] or years smoked), indicating that the impact of smoking variables on DNA adduct levels may be different in current and former smokers. Consequently, our analyses indicate that models for current and former smokers should be considered separately. In current smokers, recent smoking intensity (cigarettes smoked per day) was the most important variable. In former smokers, age at smoking initiation was inversely associated with DNA adduct levels. A highly statistically significant correlation (r=.77 [Spearman's correlation]; two sided P<.001) was observed between DNA adduct levels in blood mononuclear cells and lung tissue. IMPLICATIONS: Our results in former smokers suggest that smoking during adolescence may produce physiologic changes that lead to increased DNA adduct persistence or that young smokers may be markedly susceptible to DNA adduct formation and have higher adduct burdens after they quit smoking than those who started smoking later in life. (+info)Chromosomal aberrations in humans induced by urban air pollution: influence of DNA repair and polymorphisms of glutathione S-transferase M1 and N-acetyltransferase 2. (7/1869)
We have studied the influence of individual susceptibility factors on the genotoxic effects of urban air pollution in 106 nonsmoking bus drivers and 101 postal workers in the Copenhagen metropolitan area. We used the frequency of chromosomal aberrations in peripheral blood lymphocytes as a biomarker of genotoxic damage and dimethylsulfate-induced unscheduled DNA synthesis in mononuclear WBCs, the glutathione S-transferase M1 (GSTM1) genotype, and the N-acetyltransferase 2 (NAT2) genotype as biomarkers of susceptibility. The bus drivers, who had previously been observed to have elevated levels of aromatic DNA adducts in their peripheral mononuclear cells, showed a significantly higher frequency of cells with chromosomal aberrations as compared with the postal workers. In the bus drivers, unscheduled DNA synthesis correlated negatively with the number of cells with gaps, indicating a protective effect of DNA repair toward chromosome damage. Bus drivers with the GSTM1 null and slow acetylator NAT2 genotype had an increased frequency of cells with chromosomal aberrations. NAT2 slow acetylators also showed elevated chromosomal aberration counts among the postal workers. Our results suggest that long-term exposure to urban air pollution (with traffic as the main contributor) induces chromosome damage in human somatic cells. Low DNA repair capacity and GSTM1 and NAT2 variants associated with reduced detoxification ability increase susceptibility to such damage. The effect of the GSTM1 genotype, which was observed only in the bus drivers, appears to be associated with air pollution, whereas the NAT2 genotype effect, which affected all subjects, may influence the individual response to some other common exposure or the baseline level of chromosomal aberrations. (+info)Hip fractures among infertile women. (8/1869)
A retrospective cohort study was conducted in a population-based inception cohort of 1,157 Olmsted County, Minnesota, women with infertility (failure to conceive after 1 year despite intercourse without contraception) that was first diagnosed at the Mayo Clinic (Rochester, Minnesota) between 1935 and 1964. In this relatively young cohort, 31 hip fractures were observed during 35,849 person-years of follow-up; 36.5 had been expected (standardized incidence ratio = 0.85, 95% confidence interval 0.58-1.20). Standardized incidence ratios did not differ by type or cause of infertility. The data suggested that women with consistently irregular menses may have a greater risk of hip fracture. This finding should be confirmed by additional studies with longer follow-up periods and with assessment of other fracture outcomes. (+info)I'm sorry for any confusion, but Poisson Distribution is actually a statistical concept rather than a medical term. Here's a general definition:
Poisson Distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space, as long as these events occur with a known average rate and independently of each other. It is often used in fields such as physics, engineering, economics, and medical research to model rare events or low-probability phenomena.
In the context of medical research, Poisson Distribution might be used to analyze the number of adverse events that occur during a clinical trial, the frequency of disease outbreaks in a population, or the rate of successes or failures in a series of experiments.
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.
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.
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.
I'm sorry for any confusion, but there seems to be a misunderstanding. Mathematics is not a medical term; it is a branch of science dedicated to the study of numbers, shapes, and structures. However, mathematics does have many applications in medicine, such as in modeling disease spread, analyzing medical images, or designing clinical trials. If you have any questions related to mathematics in a medical context, I'd be happy to help clarify those for you!
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.
In epidemiology, the incidence of a disease is defined as the number of new cases of that disease within a specific population over a certain period of time. It is typically expressed as a rate, with the number of new cases in the numerator and the size of the population at risk in the denominator. Incidence provides information about the risk of developing a disease during a given time period and can be used to compare disease rates between different populations or to monitor trends in disease occurrence over time.
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.
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.
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.
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.
Poisson distribution
Mixed Poisson distribution
Poisson binomial distribution
Geometric Poisson distribution
Poisson-Dirichlet distribution
Compound Poisson distribution
Displaced Poisson distribution
Conway-Maxwell-Poisson distribution
Zero-truncated Poisson distribution
Poisson games
Poisson point process
Siméon Denis Poisson
Poisson limit theorem
Poisson sampling
Poisson's equation
Poisson scatter theorem
Poisson clumping
Statistics education
Cumulant
Rape in India
Factorial
Poisson-type random measure
Abraham de Moivre
Stochastic simulation
Poisson wavelet
Poisson number
Statistical association football predictions
Clustering illusion
Robbins lemma
Cramér's decomposition theorem
Poisson distribution - Wikipedia
Poisson distribution formular
Poisson Distribution: Interactive Tool | Mathematical Association of America
The Poisson Distribution • SOGA-Py • Department of Earth Sciences
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probability - What is the intuition behind the Poisson distribution's function? - Mathematics Stack Exchange
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Fit Custom Distributions - MATLAB & Simulink Example
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Poisson Distribution - from Wolfram MathWorld - India Dictionary
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MathsNet: P - The Poisson Distribution - Finding probabilities
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Stationary random graphs with prescribed iid degrees on a spatial Poisson process
Calculating the variance of integrated Poisson noise on a defined quantity
Binomial27
- The Poisson distribution is also the limit of a binomial distribution, for which the probability of success for each trial equals λ divided by the number of trials, as the number of trials approaches infinity (see Related distributions). (wikipedia.org)
- In other discrete distributions, namely the binomial, geometric, negative binomial, and hypergeometric distributions, I have an intuitive, combinatorics-based understanding of why each distribution's pmf is defined the way it is. (stackexchange.com)
- e^{-\lambda} $$ In other words, as the probability of success becomes a rate applied to a continuum, as opposed to discrete selections, the binomial becomes the Poisson. (stackexchange.com)
- begingroup$ So the only intuition behind the equation itself is that it's the limit as $n\to\infty$ and $p\to 0$ of the binomial distribution? (stackexchange.com)
- The Poisson binomial distribution is a probability distribution that has numerous applications in many fields of study. (probabilityhowto.com)
- In this blog post, we're going to delve into the Poisson binomial distribution, its properties, and its applications. (probabilityhowto.com)
- The Poisson binomial distribution (PBD), first studied by S. Poisson in 1837 [1] are a natural n -parameter generalization of the Binomial Distribution. (probabilityhowto.com)
- It is more flexible than the Bernoulli and binomial distributions since it can handle Success/Failure trials with different probabilities of success. (probabilityhowto.com)
- The probability mass function (PMF) of the Poisson binomial distribution can be summed up as follows: for a given n trials, each of which has a probability of success p i , the Poisson binomial distribution describes the probability of having k successes. (probabilityhowto.com)
- The Poisson binomial distribution arises in many settings such as its tail bounds form a special case of Chernoff/Hoeffding bounds [4, 5, 6]. (probabilityhowto.com)
- Additionally, in finance, the Poisson binomial distribution is used to model the risk of multiple asset investments. (probabilityhowto.com)
- Given the simplicity and ubiquity of the Poisson binomial distributions, it may be surprising to learn that problem of density estimation for PBDs is not well understood. (probabilityhowto.com)
- As such solving the Poisson binomial distribution is not a trivial task but certain approximations can be made. (probabilityhowto.com)
- When the number of trials is small, the Poisson binomial distribution can be approximated by the Bernoulli distribution . (probabilityhowto.com)
- When the probability of success in each trial is very close to 0 or 1, the Poisson binomial distribution can be approximated by the Poisson distribution. (probabilityhowto.com)
- Monte Carlo methods can be used, which is a simulation-based approach, as well as Fourier methods which compute the Poisson binomial cumulative distribution function explicitly. (probabilityhowto.com)
- Algorithms have been developed based on the premise that every Poisson binomial distribution is either close to a PBD with sparse support, or is close to a translated "heavy" Binomial distribution [2]. (probabilityhowto.com)
- In conclusion, the Poisson binomial distribution is a powerful and flexible distribution that can be used to model numerous phenomena in different fields. (probabilityhowto.com)
- The difference is very refined it is that, binomial distribution is for discrete trials, whereas poisson distribution is for steady trials. (1investing.in)
- Both the hypergeometric distribution and the binomial distribution describe the number of instances an event happens in a set number of trials. (1investing.in)
- For the binomial distribution, the likelihood is identical for every trial. (1investing.in)
- The Binomial distribution offers the probability of getting some number of successes amongst numerous Bernoulli trials that have the identical $p$ value. (1investing.in)
- The Poisson Binomial distribution, then again, allows for various values of $p$ for every of the individual Bernoulli trials. (1investing.in)
- in this context, it's primarily relevant as a limiting case of the Binomial distribution. (1investing.in)
- This chapter introduces various distributional extensions and generalities motivated by functions of COM-Poisson random variables, including Conway-Maxwell-inspired generalizations of the Skellam distribution, binomial distribution, negative binomial distribution, the Katz class of distributions, two flexible series system life length distributions, and generalizations of the negative hypergeometric distribution. (cambridge.org)
- It also provides the pmf, quantile function, and random number generation for the Poisson binomial distribution. (ethz.ch)
- Binomial-, normal- and poisson distributions are studied. (lu.se)
Variance9
- It is shown that the distribution of the sum of a Poisson random variable and an independent approximately normally distributed integer-valued random variable can be well approximated in total variation by a translated Poisson distribution, and further that a mixed translated Poisson distribution is close to a mixed translated Poisson distribution with the same random shift but fixed variance. (uzh.ch)
- The shape parameter, which is also the mean and the variance of the distribution. (r-project.org)
- This distribution is asymmetric, which means that the mean and variance are not equal to each other. (probabilityhowto.com)
- The pattern imply of X is 54.0 and the pattern standard deviation is 95.four so that this can be a gross violation of the mean-variance legislation of the Poisson. (1investing.in)
- The Poisson solely takes the imply as a parameter, not like the Gaussian distribution, which takes the mean and the variance. (1investing.in)
- This variance to mean power law is an inherent feature of a family of statistical distributions called the Tweedie exponential dispersion models . (wikipedia.org)
- Much as the central limit theorem explains how certain types of random data converge towards the form of a normal distribution there exists a related theorem, the Tweedie convergence theorem that explains how other types of random data will converge towards the form of these Tweedie distributions, and consequently express both the variance to mean power law and a power law decay in their autocorrelation functions. (wikipedia.org)
- In summary, the conversation discusses the estimation of the variance expression of Poisson noise on a quantity that is calculated through a sum of terms. (physicsforums.com)
- I want to estimate the variance expression of Poisson Noise of this qantity. (physicsforums.com)
Lambda7
- λ = E ( X ) = Var ( X ) . {\displaystyle \lambda =\operatorname {E} (X)=\operatorname {Var} (X).} The Poisson distribution can be applied to systems with a large number of possible events, each of which is rare. (wikipedia.org)
- By the definition of Poisson distribution, if in a given interval, the expected number of occurrences of some event is $\lambda$, the probability that there is exactly $k$ such events happening is $$ \frac {\lambda^k e^{-\lambda}}{k! (stackexchange.com)
- Then the probability that the Poisson variable $X_n$ with parameter $\lambda$ takes a value between $0$ and $n$ is $$ \mathbb P(X_n \le n) = e^{-n} \sum_{k=0}^n \frac{n^k}{k! (stackexchange.com)
- When it is infinite, but with finite probability $np=\lambda$ , it is Poisson. (stackexchange.com)
- Then $X$ has the Poisson distribution \[p(x)=\frac{\lambda^{x}e^{-\lambda}}{x! (matchmaticians.com)
- The Poisson Pdf computes a probability for a discrete Poisson distribution with a specified mean lambda. (ti.com)
- Poisson Cdf is used to calculate Poisson distribution cumulative probability with specified mean lambda. (ti.com)
Derivation of the Poisson distribution2
- This kind of reasoning led Clarke to a proper derivation of the Poisson distribution as a model. (1investing.in)
- The video completes the derivation of the Poisson distribution that was begun in the Poisson Process 1video. (maa.org)
Properties of the Poisson distribution1
- For example, from the above definition, we can infer that increments of the homogeneous Poisson process are stationary due to the properties of the Poisson distribution. (hpaulkeeler.com)
Approximation4
- Using these two results, a general approach is then presented for the approximation of sums of integer-valued random variables, having some conditional independence structure, by a translated Poisson distribution. (uzh.ch)
- We develop an information-theoretic foundation for compound Poisson approximation and limit theorems (analogous to the corresponding developments for the central limit theorem and for simple Poisson approximation). (mit.edu)
- Second, approximation bounds in the (strong) relative entropy sense are given for distributional approximation of sums of independent nonnegative integer valued random variables by compound Poisson distributions. (mit.edu)
- The proof techniques involve the use of a notion of local information quantities that generalize the classical Fisher information used for normal approximation, as well as the use of ingredients from Stein's method for compound Poisson approximation. (mit.edu)
Compute2
- Statistics Helper's Poisson Probability Calculator is an excellent tool designed to compute Poisson probabilities with precision and ease. (projectmanagers.net)
- function to compute maximum likelihood parameter estimates and to estimate their precision for built-in distributions and custom distributions. (mathworks.com)
Statistical4
- In statistical analysis, the Poisson distribution plays a pivotal role, particularly when predicting the probability of a given number of events happening within a set period. (projectmanagers.net)
- In statistics, a Poisson distribution is a statistical distribution that shows how many times an event is likely to occur within a specified period of time. (1investing.in)
- Statistical significance (P value) of results was based upon the Poisson distribution. (cdc.gov)
- Statistical description of distributions and motions. (lu.se)
Follow a poisson distribution2
- Free Poisson Distribution Calculator - Calculates the probability of 3 separate events that follow a poisson distribution. (mathcelebrity.com)
- means clustering, but with the added knowledge that the cluster sizes should follow a Poisson distribution. (mathematica-journal.com)
Distribution's2
- What is the intuition behind the Poisson distribution's function? (stackexchange.com)
- I'm trying to intuitively understand the Poisson distribution's probability mass function. (stackexchange.com)
Regression models1
- Analysis: We examined distributions and Poisson regression models of availability for supports by employer size and by industry and use of supports by employer size and personal factors. (cdc.gov)
Parameter3
- It is perhaps the simplest n -parameter probability distribution with some nontrivial structure [2]. (probabilityhowto.com)
- th quantile of the distribution assuming the true value of the parameter is equal to the upper confidence limit. (r-project.org)
- It can be shown that all distributions that are one parameter exponential families have the MLR property, and the Poisson distribution is a one-parameter exponential family, so the method of Zacks (1970) can be applied to a Poisson distribution. (r-project.org)
Central limit t1
- begingroup$ Second hint, to supplement the Poisson hint: central limit theorem. (stackexchange.com)
Probabilities5
- However, accurately calculating Poisson probabilities can be a complex task, necessitating specialized calculators. (projectmanagers.net)
- Stat Trek's Poisson Distribution Calculator is a remarkable tool designed for ease and efficiency in computing Poisson probabilities. (projectmanagers.net)
- This online calculator stands out for its user-friendly interface, allowing users to enter values and obtain individual and cumulative Poisson probabilities easily. (projectmanagers.net)
- The University of Iowa's Poisson Distribution Applet is a sophisticated yet user-friendly tool designed for computing probabilities associated with the Poisson distribution. (projectmanagers.net)
- A long-tailed or heavy-tailed distribution is one that assigns relatively high probabilities to regions far from the mean or median. (wikipedia.org)
Zero-truncated6
- You need to define the zero-truncated Poisson distribution by its probability mass function (pmf). (mathworks.com)
- The pmf for a zero-truncated Poisson distribution is the Poisson pmf normalized so that it sums to one. (mathworks.com)
- Recently, the zero-truncated Poisson-Lindley distribution has been proposed for studying count data containing non-zero values. (tci-thaijo.org)
- Last, the nonparametric bootstrap confidence intervals were used to calculate the confidence interval for the population mean of the zero-truncated Poisson-Lindley distribution via two numerical examples, the results of which match those from the simulation study. (tci-thaijo.org)
- Zero-truncated Poisson-Lindley distribution and its application. (tci-thaijo.org)
- A zero truncated discrete distribution: Theory and applications to count data. (tci-thaijo.org)
Hypergeometric distribution1
- For the hypergeometric distribution, each trial changes the chance for every subsequent trial because there is no substitute. (1investing.in)
20221
- In this study, inspired by the work of Richman and Wuthrich (2021) and extending on our recent work by Tzougas and Li (2022), we introduce the local mixed Poisson net, which we call LocalMPnet, for modelling claim count data using an interpretable deep learning architecture. (sheffield.ac.uk)
Bernoulli1
- It is a generalization of the well-known Bernoulli distribution and is well suited to describe the probability of success in a sequence of independent and non-identically distributed trials. (probabilityhowto.com)
Summation1
- The Poisson summation formula (PSF), which relates the sampling of an analog signal with the periodization of its Fourier transform, plays a key role in the classical sampling theory. (epfl.ch)
Probability theory2
- In probability theory and statistics, the Poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant mean rate and independently of the time since the last event. (wikipedia.org)
- The distribution was first introduced by Siméon Denis Poisson (1781-1840) and published together with his probability theory in his work Recherches sur la probabilité des jugements en matière criminelle et en matière civile (1837). (wikipedia.org)
Calculate2
- Using a Poisson distribution with a probability of success of 0.4, calculate the Probability of having exactly 0 successes in 10 tries. (mathcelebrity.com)
- Solution 29450: How to Calculate the Poisson Pdf and Poisson Cdf on the TI-Nspire™ Family Line of Products. (ti.com)
Formula1
- As you can see from the screenshot above, Nickzom Calculator - The Calculator Encyclopedia solves for the poisson probability distribution and presents the formula, workings and steps too. (nickzom.org)
Successes1
- Find the poisson probability distribution when the mean of the theoretical distribution is 12 and the number of successes of event A is 6. (nickzom.org)
Counts4
- Poisson distributions are frequently used to model counts. (r-project.org)
- However, in some situations, counts that are zero are not recorded in the data, so fitting a Poisson distribution is not straightforward because of the missing zeros. (mathworks.com)
- Neural Network Embedding of the Mixed Poisson Regression Model for Claim Counts. (sheffield.ac.uk)
- the EAPCs in case counts were calculated by using a Poisson distribution. (cdc.gov)
Estimate2
- A Poisson distribution can be utilized to estimate how doubtless it is that one thing will happen "X" variety of occasions. (1investing.in)
- Logistic-regression analysis and Poisson regression analysis were used to estimate changes between the two three-year periods, after adjustment for the above-mentioned determinants of the likelihood of preterm births. (nih.gov)
Need to define1
- To fit a custom distribution, you need to define a function for the custom distribution in a file or by using an anonymous function. (mathworks.com)
Implementation2
- means algorithm to scenarios in which the ideal distribution that the clusters should follow is known, and though some of the implementation is specific to the context of TES calibration (e.g. the use of the Poisson distribution, the idea of ordering observations by photon number), much of it can be generalized without much difficulty to other situations with known probability distributions. (mathematica-journal.com)
- This is a lua implementation of the algorithm described in -- http://devmag.org.za/2009/05/03/poisson-disk-sampling/ -- -- The structure of the algorithm is exactly the same than in -- the mentioned article. (stackexchange.com)
Likelihood1
- the likelihood that a Poisson random variable is equal to a given rely. (1investing.in)
Begingroup1
- begingroup$ To apply the answer you referenced, you need to take $n_1=n_2=1$ because you have exactly one observation from each distribution. (stackexchange.com)
Calculator7
- How does the Poisson Distribution Calculator work? (mathcelebrity.com)
- What 2 formulas are used for the Poisson Distribution Calculator? (mathcelebrity.com)
- What 9 concepts are covered in the Poisson Distribution Calculator? (mathcelebrity.com)
- To use the calculator, one inputs values into two unshaded text boxes: the Poisson random variable (x) and the average rate of success (μ). (projectmanagers.net)
- This calculator is especially useful for students and professionals who require quick and accurate Poisson probability calculations. (projectmanagers.net)
- This combination of simplicity, comprehensive functionality, and educational support positions Stat Trek's Poisson Distribution Calculator as a top choice for anyone working with Poisson distribution. (projectmanagers.net)
- Nickzom Calculator - The Calculator Encyclopedia is capable of calculating the poisson probability distribution. (nickzom.org)
Interval5
- The Poisson distribution can also be used for the number of events in other specified interval types such as distance, area, or volume. (wikipedia.org)
- The number of such events that occur during a fixed time interval is, under the right circumstances, a random number with a Poisson distribution. (wikipedia.org)
- For instance, the Poisson distribution is appropriate for modeling the variety of phone calls an workplace would receive through the noon hour, in the event that they know that they common four calls per hour throughout that time interval. (1investing.in)
- the interval [0, 4] contains 94.7% of this distribution and the interval [0, 5] contains 98.3% of this distribution. (r-project.org)
- Thus, no interval can contain exactly 95% of this distribution. (r-project.org)
Examples1
- It can be tough to find out whether or not a random variable truly has a Poisson distribution, so right here I look at a few examples and some visual illustrations that may assist. (1investing.in)
Random variable2
- If these conditions are true, then k is a Poisson random variable, and the distribution of k is a Poisson distribution. (wikipedia.org)
- A not-too-technical have a look at the conditions required for a random variable to have a Poisson distribution. (1investing.in)
Spatial1
- Maria Deijfen "Stationary random graphs with prescribed iid degrees on a spatial Poisson process," Electronic Communications in Probability, Electron. (projecteuclid.org)
Compound1
- First, su?cient conditions are given under which the compound Poisson distribution has maximal entropy within a natural class of probability measures on the nonnegative integers. (mit.edu)
Generate3
- First, generate some random Poisson data. (mathworks.com)
- In this answer by @Jake to the question Filling specified area by random dots in TikZ I learned about the poisson disc sampling technique to generate nice looking random patterns. (stackexchange.com)
- The candidate particles, ranging from protons to nuclei as massive as iron, generate "extensive air-showers" (EAS) in interactions with air nuclei when en- tering the Earth's atmosphere. (lu.se)
Model3
- For example, geneticists use this distribution to model the evolution of traits in a population, while epidemiologists use it to model the spread of diseases. (probabilityhowto.com)
- Mandelbrot established the use of heavy-tail distributions to model real-world fractal phenomena, e.g. (wikipedia.org)
- In this article, an attempt has been made to model and analyze the proposed inspection method through STDS plan, when the number of defect is less, which follows a ZIP distribution. (mathsjournal.com)
Theory1
- In some literature, such as the theory of Lévy processes, a Poisson point process is called a Poisson random measure, differentiating the Poisson point process from the Poisson stochastic process. (hpaulkeeler.com)
Identical1
- You can use a custom distribution that is identical to a Poisson distribution on the positive integers, but has no probability at zero. (mathworks.com)
Quantile1
- th quantile of this distribution. (r-project.org)
Observations1
- numeric vector of observations, or an object resulting from a call to an estimating function that assumes a Poisson distribution (i.e. (r-project.org)
Search1
- Input a term hyper poisson distribution by either copy & post, drag & drop, or simply by typing in the search box. (khandbahale.com)
Process12
- Think about a Poisson process. (stackexchange.com)
- One of the most important stochastic processes is Poisson stochastic process, often called simply the Poisson process. (hpaulkeeler.com)
- The Poisson (stochastic) process is a counting process. (hpaulkeeler.com)
- The points in time when a Poisson stochastic process increases form a Poisson point process on the real line. (hpaulkeeler.com)
- The Poisson point process is often just called the Poisson process , but a Poisson point process can be defined on more generals spaces. (hpaulkeeler.com)
- In this post I will give a definition of the homogenous Poisson process . (hpaulkeeler.com)
- In the stochastic processes literature there are different definitions of the Poisson process. (hpaulkeeler.com)
- The definition of the Poisson (stochastic) process means that it has stationary and independent increments. (hpaulkeeler.com)
- The Poisson (stochastic) process exhibits closure properties, meaning you apply certain operations, you get another Poisson (stochastic) process. (hpaulkeeler.com)
- A single realization of a (homogeneous) Poisson stochastic process, where the blue marks show where the process jumps to the next value. (hpaulkeeler.com)
- This is to be contrasted with telephone traffic which is Poisson in its arrival and departure process. (wikipedia.org)
- Let $[\mathcal{P}]$ be the points of a Poisson process on $R^d$ and $F$ a probability distribution with support on the non-negative integers. (projecteuclid.org)
Content1
- Its combination of functionality, educational content, and ease of use positions it as an essential tool for anyone working with or studying the Poisson distribution. (projectmanagers.net)