**Chi-Square Distribution**: A distribution in which a variable is distributed like the sum of the squares of any given independent random variable, each of which has a normal distribution with mean of zero and variance of one. The chi-square test is a statistical test based on comparison of a test statistic to a chi-square distribution. The oldest of these tests are used to detect whether two or more population distributions differ from one another.

**India**

**Cross-Sectional Studies**: Studies in which the presence or absence of disease or other health-related variables are determined in each member of the study population or in a representative sample at one particular time. This contrasts with LONGITUDINAL STUDIES which are followed over a period of time.

**Questionnaires**: Predetermined sets of questions used to collect data - clinical data, social status, occupational group, etc. The term is often applied to a self-completed survey instrument.

**Retrospective Studies**: Studies used to test etiologic hypotheses in which inferences about an exposure to putative causal factors are derived from data relating to characteristics of persons under study or to events or experiences in their past. The essential feature is that some of the persons under study have the disease or outcome of interest and their characteristics are compared with those of unaffected persons.

**Prevalence**: The total number of cases of a given disease in a specified population at a designated time. It is differentiated from INCIDENCE, which refers to the number of new cases in the population at a given time.

**Turkey**

**Least-Squares Analysis**: A principle of estimation in which the estimates of a set of parameters in a statistical model are those quantities minimizing the sum of squared differences between the observed values of a dependent variable and the values predicted by the model.

**Logistic Models**: Statistical models which describe the relationship between a qualitative dependent variable (that is, one which can take only certain discrete values, such as the presence or absence of a disease) and an independent variable. A common application is in epidemiology for estimating an individual's risk (probability of a disease) as a function of a given risk factor.

**Risk Factors**: An aspect of personal behavior or lifestyle, environmental exposure, or inborn or inherited characteristic, which, on the basis of epidemiologic evidence, is known to be associated with a health-related condition considered important to prevent.

**Health Knowledge, Attitudes, Practice**: Knowledge, attitudes, and associated behaviors which pertain to health-related topics such as PATHOLOGIC PROCESSES or diseases, their prevention, and treatment. This term refers to non-health workers and health workers (HEALTH PERSONNEL).

**Age Factors**: 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.

**Prospective Studies**: Observation of a population for a sufficient number of persons over a sufficient number of years to generate incidence or mortality rates subsequent to the selection of the study group.

**Treatment Outcome**: Evaluation undertaken to assess the results or consequences of management and procedures used in combating disease in order to determine the efficacy, effectiveness, safety, and practicability of these interventions in individual cases or series.

**Sex Factors**: Maleness or femaleness as a constituent element or influence contributing to the production of a result. It may be applicable to the cause or effect of a circumstance. It is used with human or animal concepts but should be differentiated from SEX CHARACTERISTICS, anatomical or physiological manifestations of sex, and from SEX DISTRIBUTION, the number of males and females in given circumstances.

**Rural Population**: The inhabitants of rural areas or of small towns classified as rural.

**Time Factors**: Elements of limited time intervals, contributing to particular results or situations.

**Follow-Up Studies**: Studies in which individuals or populations are followed to assess the outcome of exposures, procedures, or effects of a characteristic, e.g., occurrence of disease.

**Socioeconomic Factors**: Social and economic factors that characterize the individual or group within the social structure.

**Case-Control Studies**: Studies which start with the identification of persons with a disease of interest and a control (comparison, referent) group without the disease. The relationship of an attribute to the disease is examined by comparing diseased and non-diseased persons with regard to the frequency or levels of the attribute in each group.

**Prognosis**: A prediction of the probable outcome of a disease based on a individual's condition and the usual course of the disease as seen in similar situations.

**Pregnancy**: The status during which female mammals carry their developing young (EMBRYOS or FETUSES) in utero before birth, beginning from FERTILIZATION to BIRTH.

**Tai Ji**: One of the MARTIAL ARTS and also a form of meditative exercise using methodically slow circular stretching movements and positions of body balance.

**Severity of Illness Index**: Levels within a diagnostic group which are established by various measurement criteria applied to the seriousness of a patient's disorder.

**Cohort Studies**: Studies in which subsets of a defined population are identified. These groups may or may not be exposed to factors hypothesized to influence the probability of the occurrence of a particular disease or other outcome. Cohorts are defined populations which, as a whole, are followed in an attempt to determine distinguishing subgroup characteristics.

**Digestion**: The process of breakdown of food for metabolism and use by the body.

**Animal Feed**: Foodstuff used especially for domestic and laboratory animals, or livestock.

**Rumen**: The first stomach of ruminants. It lies on the left side of the body, occupying the whole of the left side of the abdomen and even stretching across the median plane of the body to the right side. It is capacious, divided into an upper and a lower sac, each of which has a blind sac at its posterior extremity. The rumen is lined by mucous membrane containing no digestive glands, but mucus-secreting glands are present in large numbers. Coarse, partially chewed food is stored and churned in the rumen until the animal finds circumstances convenient for rumination. When this occurs, little balls of food are regurgitated through the esophagus into the mouth, and are subjected to a second more thorough mastication, swallowed, and passed on into other parts of the compound stomach. (From Black's Veterinary Dictionary, 17th ed)

**Algorithms**: A procedure consisting of a sequence of algebraic formulas and/or logical steps to calculate or determine a given task.

**Reproducibility of Results**: 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.

**Computer Simulation**: Computer-based representation of physical systems and phenomena such as chemical processes.

**Models, Statistical**: 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.

**Cattle**: 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.

**Animal Nutritional Physiological Phenomena**: Nutritional physiology of animals.

**Exodeoxyribonuclease V**: An ATP-dependent exodeoxyribonuclease that cleaves in either the 5'- to 3'- or the 3'- to 5'-direction to yield 5'-phosphooligonucleotides. It is primarily found in BACTERIA.

**Nitrogen**: An element with the atomic symbol N, atomic number 7, and atomic weight [14.00643; 14.00728]. Nitrogen exists as a diatomic gas and makes up about 78% of the earth's atmosphere by volume. It is a constituent of proteins and nucleic acids and found in all living cells.

**Poaceae**: A large family of narrow-leaved herbaceous grasses of the order Cyperales, subclass Commelinidae, class Liliopsida (monocotyledons). Food grains (EDIBLE GRAIN) come from members of this family. RHINITIS, ALLERGIC, SEASONAL can be induced by POLLEN of many of the grasses.

**Fatty Acids, Volatile**: Short-chain fatty acids of up to six carbon atoms in length. They are the major end products of microbial fermentation in the ruminant digestive tract and have also been implicated in the causation of neurological diseases in humans.

**Models, Biological**: 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.

**Mathematics**: The deductive study of shape, quantity, and dependence. (From McGraw-Hill Dictionary of Scientific and Technical Terms, 6th ed)

**Models, Theoretical**: 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.

**Random Allocation**: A process involving chance used in therapeutic trials or other research endeavor for allocating experimental subjects, human or animal, between treatment and control groups, or among treatment groups. It may also apply to experiments on inanimate objects.

**Vietnam**

**Fermentation**: Anaerobic degradation of GLUCOSE or other organic nutrients to gain energy in the form of ATP. End products vary depending on organisms, substrates, and enzymatic pathways. Common fermentation products include ETHANOL and LACTIC ACID.

**Data Interpretation, Statistical**: Application of statistical procedures to analyze specific observed or assumed facts from a particular study.

**Regression Analysis**: 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.

**Sensitivity and Specificity**: 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)

**Analysis of Variance**: A statistical technique that isolates and assesses the contributions of categorical independent variables to variation in the mean of a continuous dependent variable.

**Silage**: Fodder converted into succulent feed for livestock through processes of anaerobic fermentation (as in a silo).

**Linear Models**: 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.

**Models, Molecular**: Models used experimentally or theoretically to study molecular shape, electronic properties, or interactions; includes analogous molecules, computer-generated graphics, and mechanical structures.

**Zea mays**: A plant species of the family POACEAE. It is a tall grass grown for its EDIBLE GRAIN, corn, used as food and animal FODDER.

**Genotype**: The genetic constitution of the individual, comprising the ALLELES present at each GENETIC LOCUS.

**Diet**: Regular course of eating and drinking adopted by a person or animal.

**Discriminant Analysis**: A statistical analytic technique used with discrete dependent variables, concerned with separating sets of observed values and allocating new values. It is sometimes used instead of regression analysis.

**Eating**: The consumption of edible substances.

**Dietary Fiber**: The remnants of plant cell walls that are resistant to digestion by the alimentary enzymes of man. It comprises various polysaccharides and lignins.

**Models, Genetic**: 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.

**Medicago sativa**: A plant species of the family FABACEAE widely cultivated for ANIMAL FEED.

**Spectroscopy, Near-Infrared**: A noninvasive technique that uses the differential absorption properties of hemoglobin and myoglobin to evaluate tissue oxygenation and indirectly can measure regional hemodynamics and blood flow. Near-infrared light (NIR) can propagate through tissues and at particular wavelengths is differentially absorbed by oxygenated vs. deoxygenated forms of hemoglobin and myoglobin. Illumination of intact tissue with NIR allows qualitative assessment of changes in the tissue concentration of these molecules. The analysis is also used to determine body composition.

**Signal Processing, Computer-Assisted**: Computer-assisted processing of electric, ultrasonic, or electronic signals to interpret function and activity.

**Principal Component Analysis**: Mathematical procedure that transforms a number of possibly correlated variables into a smaller number of uncorrelated variables called principal components.

**Dietary Proteins**: Proteins obtained from foods. They are the main source of the ESSENTIAL AMINO ACIDS.

**Image Processing, Computer-Assisted**: A technique of inputting two-dimensional images into a computer and then enhancing or analyzing the imagery into a form that is more useful to the human observer.

**Chromium Compounds**: Inorganic compounds that contain chromium as an integral part of the molecule.

**Statistics as Topic**: 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.

**Models, Chemical**: Theoretical representations that simulate the behavior or activity of chemical processes or phenomena; includes the use of mathematical equations, computers, and other electronic equipment.

**Multivariate Analysis**: 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.

**Calibration**: Determination, by measurement or comparison with a standard, of the correct value of each scale reading on a meter or other measuring instrument; or determination of the settings of a control device that correspond to particular values of voltage, current, frequency or other output.

**Nutritive Value**: An indication of the contribution of a food to the nutrient content of the diet. This value depends on the quantity of a food which is digested and absorbed and the amounts of the essential nutrients (protein, fat, carbohydrate, minerals, vitamins) which it contains. This value can be affected by soil and growing conditions, handling and storage, and processing.

**Protein Conformation**: The characteristic 3-dimensional shape of a protein, including the secondary, supersecondary (motifs), tertiary (domains) and quaternary structure of the peptide chain. PROTEIN STRUCTURE, QUATERNARY describes the conformation assumed by multimeric proteins (aggregates of more than one polypeptide chain).

**Swine**: Any of various animals that constitute the family Suidae and comprise stout-bodied, short-legged omnivorous mammals with thick skin, usually covered with coarse bristles, a rather long mobile snout, and small tail. Included are the genera Babyrousa, Phacochoerus (wart hogs), and Sus, the latter containing the domestic pig (see SUS SCROFA).

**Ammonia**: A colorless alkaline gas. It is formed in the body during decomposition of organic materials during a large number of metabolically important reactions. Note that the aqueous form of ammonia is referred to as AMMONIUM HYDROXIDE.

**Molasses**: The syrup remaining after sugar is crystallized out of SUGARCANE or sugar beet juice. It is also used in ANIMAL FEED, and in a fermented form, is used to make industrial ETHYL ALCOHOL and ALCOHOLIC BEVERAGES.

**Quantitative Structure-Activity Relationship**: A quantitative prediction of the biological, ecotoxicological or pharmaceutical activity of a molecule. It is based upon structure and activity information gathered from a series of similar compounds.

**Soybeans**: An annual legume. The SEEDS of this plant are edible and used to produce a variety of SOY FOODS.

**Breeding**: The production of offspring by selective mating or HYBRIDIZATION, GENETIC in animals or plants.

**Software**: Sequential operating programs and data which instruct the functioning of a digital computer.

**Chitinase**

**Public Facilities**: An area of recreation or hygiene for use by the public.

**Image Interpretation, Computer-Assisted**: Methods developed to aid in the interpretation of ultrasound, radiographic images, etc., for diagnosis of disease.

**Gene Frequency**: The proportion of one particular in the total of all ALLELES for one genetic locus in a breeding POPULATION.

**China**: A country spanning from central Asia to the Pacific Ocean.

**United States**

**Food Handling**: Any aspect of the operations in the preparation, processing, transport, storage, packaging, wrapping, exposure for sale, service, or delivery of food.

**Freeze Fracturing**: Preparation for electron microscopy of minute replicas of exposed surfaces of the cell which have been ruptured in the frozen state. The specimen is frozen, then cleaved under high vacuum at the same temperature. The exposed surface is shadowed with carbon and platinum and coated with carbon to obtain a carbon replica.

**Equipment Design**: Methods of creating machines and devices.

**Magnetic Resonance Spectroscopy**: Spectroscopic method of measuring the magnetic moment of elementary particles such as atomic nuclei, protons or electrons. It is employed in clinical applications such as NMR Tomography (MAGNETIC RESONANCE IMAGING).

**Hydrogen-Ion Concentration**: The normality of a solution with respect to HYDROGEN ions; H+. It is related to acidity measurements in most cases by pH = log 1/2[1/(H+)], where (H+) is the hydrogen ion concentration in gram equivalents per liter of solution. (McGraw-Hill Dictionary of Scientific and Technical Terms, 6th ed)

**Exodeoxyribonucleases**: A family of enzymes that catalyze the exonucleolytic cleavage of DNA. It includes members of the class EC 3.1.11 that produce 5'-phosphomonoesters as cleavage products.

**Predictive Value of Tests**: In screening and diagnostic tests, the probability that a person with a positive test is a true positive (i.e., has the disease), is referred to as the predictive value of a positive test; whereas, the predictive value of a negative test is the probability that the person with a negative test does not have the disease. Predictive value is related to the sensitivity and specificity of the test.

**Temperature**: The property of objects that determines the direction of heat flow when they are placed in direct thermal contact. The temperature is the energy of microscopic motions (vibrational and translational) of the particles of atoms.

**Normal Distribution**: 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.

**Photic Stimulation**: Investigative technique commonly used during ELECTROENCEPHALOGRAPHY in which a series of bright light flashes or visual patterns are used to elicit brain activity.

**Escherichia coli**: A species of gram-negative, facultatively anaerobic, rod-shaped bacteria (GRAM-NEGATIVE FACULTATIVELY ANAEROBIC RODS) commonly found in the lower part of the intestine of warm-blooded animals. It is usually nonpathogenic, but some strains are known to produce DIARRHEA and pyogenic infections. Pathogenic strains (virotypes) are classified by their specific pathogenic mechanisms such as toxins (ENTEROTOXIGENIC ESCHERICHIA COLI), etc.

**X-Ray Diffraction**: The scattering of x-rays by matter, especially crystals, with accompanying variation in intensity due to interference effects. Analysis of the crystal structure of materials is performed by passing x-rays through them and registering the diffraction image of the rays (CRYSTALLOGRAPHY, X-RAY). (From McGraw-Hill Dictionary of Scientific and Technical Terms, 4th ed)

**Kinetics**: The rate dynamics in chemical or physical systems.

**Congenital Hyperinsulinism**: A familial, nontransient HYPOGLYCEMIA with defects in negative feedback of GLUCOSE-regulated INSULIN release. Clinical phenotypes include HYPOGLYCEMIA; HYPERINSULINEMIA; SEIZURES; COMA; and often large BIRTH WEIGHT. Several sub-types exist with the most common, type 1, associated with mutations on an ATP-BINDING CASSETTE TRANSPORTERS (subfamily C, member 8).

**Amino Acids**: Organic compounds that generally contain an amino (-NH2) and a carboxyl (-COOH) group. Twenty alpha-amino acids are the subunits which are polymerized to form proteins.

**Pattern Recognition, Visual**: Mental process to visually perceive a critical number of facts (the pattern), such as characters, shapes, displays, or designs.

**Likelihood Functions**: 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.

**Sheep**: Any of the ruminant mammals with curved horns in the genus Ovis, family Bovidae. They possess lachrymal grooves and interdigital glands, which are absent in GOATS.

**Factor Analysis, Statistical**: A set of statistical methods for analyzing the correlations among several variables in order to estimate the number of fundamental dimensions that underlie the observed data and to describe and measure those dimensions. It is used frequently in the development of scoring systems for rating scales and questionnaires.

**Electrodes**: Electric conductors through which electric currents enter or leave a medium, whether it be an electrolytic solution, solid, molten mass, gas, or vacuum.

**Alleles**: Variant forms of the same gene, occupying the same locus on homologous CHROMOSOMES, and governing the variants in production of the same gene product.

**Duodenum**: The shortest and widest portion of the SMALL INTESTINE adjacent to the PYLORUS of the STOMACH. It is named for having the length equal to about the width of 12 fingers.

**Neural Networks (Computer)**: A computer architecture, implementable in either hardware or software, modeled after biological neural networks. Like the biological system in which the processing capability is a result of the interconnection strengths between arrays of nonlinear processing nodes, computerized neural networks, often called perceptrons or multilayer connectionist models, consist of neuron-like units. A homogeneous group of units makes up a layer. These networks are good at pattern recognition. They are adaptive, performing tasks by example, and thus are better for decision-making than are linear learning machines or cluster analysis. They do not require explicit programming.

**Starch**: Any of a group of polysaccharides of the general formula (C6-H10-O5)n, composed of a long-chain polymer of glucose in the form of amylose and amylopectin. It is the chief storage form of energy reserve (carbohydrates) in plants.

**Polymorphism, Genetic**: The regular and simultaneous occurrence in a single interbreeding population of two or more discontinuous genotypes. The concept includes differences in genotypes ranging in size from a single nucleotide site (POLYMORPHISM, SINGLE NUCLEOTIDE) to large nucleotide sequences visible at a chromosomal level.

**Image Enhancement**: Improvement of the quality of a picture by various techniques, including computer processing, digital filtering, echocardiographic techniques, light and ultrastructural MICROSCOPY, fluorescence spectrometry and microscopy, scintigraphy, and in vitro image processing at the molecular level.

**Genetic Predisposition to Disease**: A latent susceptibility to disease at the genetic level, which may be activated under certain conditions.

**Contrast Sensitivity**: The ability to detect sharp boundaries (stimuli) and to detect slight changes in luminance at regions without distinct contours. Psychophysical measurements of this visual function are used to evaluate visual acuity and to detect eye disease.

**Monte Carlo Method**: 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)

**Feces**: Excrement from the INTESTINES, containing unabsorbed solids, waste products, secretions, and BACTERIA of the DIGESTIVE SYSTEM.

**Nonlinear Dynamics**: The study of systems which respond disproportionately (nonlinearly) to initial conditions or perturbing stimuli. Nonlinear systems may exhibit "chaos" which is classically characterized as sensitive dependence on initial conditions. Chaotic systems, while distinguished from more ordered periodic systems, are not random. When their behavior over time is appropriately displayed (in "phase space"), constraints are evident which are described by "strange attractors". Phase space representations of chaotic systems, or strange attractors, usually reveal fractal (FRACTALS) self-similarity across time scales. Natural, including biological, systems often display nonlinear dynamics and chaos.

**Magnetic Resonance Imaging**: Non-invasive method of demonstrating internal anatomy based on the principle that atomic nuclei in a strong magnetic field absorb pulses of radiofrequency energy and emit them as radiowaves which can be reconstructed into computerized images. The concept includes proton spin tomographic techniques.

**Heart Rate**: The number of times the HEART VENTRICLES contract per unit of time, usually per minute.

**Mathematical Computing**: Computer-assisted interpretation and analysis of various mathematical functions related to a particular problem.

**Polymorphism, Single Nucleotide**: A single nucleotide variation in a genetic sequence that occurs at appreciable frequency in the population.

**Size Perception**: The sensory interpretation of the dimensions of objects.

**Solutions**: The homogeneous mixtures formed by the mixing of a solid, liquid, or gaseous substance (solute) with a liquid (the solvent), from which the dissolved substances can be recovered by physical processes. (From Grant & Hackh's Chemical Dictionary, 5th ed)

**Probability**: The study of chance processes or the relative frequency characterizing a chance process.

**Molecular Sequence Data**: Descriptions of specific amino acid, carbohydrate, or nucleotide sequences which have appeared in the published literature and/or are deposited in and maintained by databanks such as GENBANK, European Molecular Biology Laboratory (EMBL), National Biomedical Research Foundation (NBRF), or other sequence repositories.

**Water**: A clear, odorless, tasteless liquid that is essential for most animal and plant life and is an excellent solvent for many substances. The chemical formula is hydrogen oxide (H2O). (McGraw-Hill Dictionary of Scientific and Technical Terms, 4th ed)

**Weight Gain**: Increase in BODY WEIGHT over existing weight.

**Fourier Analysis**: Analysis based on the mathematical function first formulated by Jean-Baptiste-Joseph Fourier in 1807. The function, known as the Fourier transform, describes the sinusoidal pattern of any fluctuating pattern in the physical world in terms of its amplitude and its phase. It has broad applications in biomedicine, e.g., analysis of the x-ray crystallography data pivotal in identifying the double helical nature of DNA and in analysis of other molecules, including viruses, and the modified back-projection algorithm universally used in computerized tomography imaging, etc. (From Segen, The Dictionary of Modern Medicine, 1992)

**Psychophysics**: The science dealing with the correlation of the physical characteristics of a stimulus, e.g., frequency or intensity, with the response to the stimulus, in order to assess the psychologic factors involved in the relationship.

**Toxocara**: A genus of ascarid nematodes commonly parasitic in the intestines of cats and dogs.

**Ileum**: The distal and narrowest portion of the SMALL INTESTINE, between the JEJUNUM and the ILEOCECAL VALVE of the LARGE INTESTINE.

**Phantoms, Imaging**: Devices or objects in various imaging techniques used to visualize or enhance visualization by simulating conditions encountered in the procedure. Phantoms are used very often in procedures employing or measuring x-irradiation or radioactive material to evaluate performance. Phantoms often have properties similar to human tissue. Water demonstrates absorbing properties similar to normal tissue, hence water-filled phantoms are used to map radiation levels. Phantoms are used also as teaching aids to simulate real conditions with x-ray or ultrasonic machines. (From Iturralde, Dictionary and Handbook of Nuclear Medicine and Clinical Imaging, 1990)

**Motion**: Physical motion, i.e., a change in position of a body or subject as a result of an external force. It is distinguished from MOVEMENT, a process resulting from biological activity.

**Dietary Supplements**: Products in capsule, tablet or liquid form that provide dietary ingredients, and that are intended to be taken by mouth to increase the intake of nutrients. Dietary supplements can include macronutrients, such as proteins, carbohydrates, and fats; and/or MICRONUTRIENTS, such as VITAMINS; MINERALS; and PHYTOCHEMICALS.

**Postural Balance**: A POSTURE in which an ideal body mass distribution is achieved. Postural balance provides the body carriage stability and conditions for normal functions in stationary position or in movement, such as sitting, standing, or walking.

**Electricity**: The physical effects involving the presence of electric charges at rest and in motion.

**Computers**

**Hordeum**: A plant genus of the family POACEAE. The EDIBLE GRAIN, barley, is widely used as food.

**Reference Values**: 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.

**Artifacts**: Any visible result of a procedure which is caused by the procedure itself and not by the entity being analyzed. Common examples include histological structures introduced by tissue processing, radiographic images of structures that are not naturally present in living tissue, and products of chemical reactions that occur during analysis.

**Double-Blind Method**: A method of studying a drug or procedure in which both the subjects and investigators are kept unaware of who is actually getting which specific treatment.

**Thermodynamics**: A rigorously mathematical analysis of energy relationships (heat, work, temperature, and equilibrium). It describes systems whose states are determined by thermal parameters, such as temperature, in addition to mechanical and electromagnetic parameters. (From Hawley's Condensed Chemical Dictionary, 12th ed)

**Lighting**: The illumination of an environment and the arrangement of lights to achieve an effect or optimal visibility. Its application is in domestic or in public settings and in medical and non-medical environments.

**Signal-To-Noise Ratio**: The comparison of the quantity of meaningful data to the irrelevant or incorrect data.

**Proteins**: Linear POLYPEPTIDES that are synthesized on RIBOSOMES and may be further modified, crosslinked, cleaved, or assembled into complex proteins with several subunits. The specific sequence of AMINO ACIDS determines the shape the polypeptide will take, during PROTEIN FOLDING, and the function of the protein.

**Corneal Topography**: The measurement of curvature and shape of the anterior surface of the cornea using techniques such as keratometry, keratoscopy, photokeratoscopy, profile photography, computer-assisted image processing and videokeratography. This measurement is often applied in the fitting of contact lenses and in diagnosing corneal diseases or corneal changes including keratoconus, which occur after keratotomy and keratoplasty.

**Optical Illusions**: An illusion of vision usually affecting spatial relations.

**Photometry**: Measurement of the various properties of light.

**Equipment Failure Analysis**: The evaluation of incidents involving the loss of function of a device. These evaluations are used for a variety of purposes such as to determine the failure rates, the causes of failures, costs of failures, and the reliability and maintainability of devices.

**Body Weight**: The mass or quantity of heaviness of an individual. It is expressed by units of pounds or kilograms.

**Intramolecular Lyases**: Enzymes of the isomerase class that catalyze reactions in which a group can be regarded as eliminated from one part of a molecule, leaving a double bond, while remaining covalently attached to the molecule. (From Enzyme Nomenclature, 1992) EC 5.5.

**Animal Husbandry**: The science of breeding, feeding and care of domestic animals; includes housing and nutrition.

**Mastication**: The act and process of chewing and grinding food in the mouth.

**Transducers**: Any device or element which converts an input signal into an output signal of a different form. Examples include the microphone, phonographic pickup, loudspeaker, barometer, photoelectric cell, automobile horn, doorbell, and underwater sound transducer. (McGraw Hill Dictionary of Scientific and Technical Terms, 4th ed)

**Diffusion**: The tendency of a gas or solute to pass from a point of higher pressure or concentration to a point of lower pressure or concentration and to distribute itself throughout the available space. Diffusion, especially FACILITATED DIFFUSION, is a major mechanism of BIOLOGICAL TRANSPORT.

**Incidence**: The number of new cases of a given disease during a given period in a specified population. It also is used for the rate at which new events occur in a defined population. It is differentiated from PREVALENCE, which refers to all cases, new or old, in the population at a given time.

**Surface Properties**: Characteristics or attributes of the outer boundaries of objects, including molecules.

**Support Vector Machines**: Learning algorithms which are a set of related supervised computer learning methods that analyze data and recognize patterns, and used for classification and regression analysis.

**Head Injuries, Closed**: Traumatic injuries to the cranium where the integrity of the skull is not compromised and no bone fragments or other objects penetrate the skull and dura mater. This frequently results in mechanical injury being transmitted to intracranial structures which may produce traumatic brain injuries, hemorrhage, or cranial nerve injury. (From Rowland, Merritt's Textbook of Neurology, 9th ed, p417)

**Crystallography, X-Ray**: The study of crystal structure using X-RAY DIFFRACTION techniques. (McGraw-Hill Dictionary of Scientific and Technical Terms, 4th ed)

**Cereals**: Seeds from grasses (POACEAE) which are important in the diet.

**Stomach, Ruminant**

**Infant, Newborn**: An infant during the first month after birth.

**Molecular Conformation**: The characteristic three-dimensional shape of a molecule.

**Visual Perception**: The selecting and organizing of visual stimuli based on the individual's past experience.

**Molecular Structure**: The location of the atoms, groups or ions relative to one another in a molecule, as well as the number, type and location of covalent bonds.

**Biophysics**: The study of PHYSICAL PHENOMENA and PHYSICAL PROCESSES as applied to living things.

**Metabolomics**: The systematic identification and quantitation of all the metabolic products of a cell, tissue, organ, or organism under varying conditions. The METABOLOME of a cell or organism is a dynamic collection of metabolites which represent its net response to current conditions.

**Body Mass Index**: An indicator of body density as determined by the relationship of BODY WEIGHT to BODY HEIGHT. BMI=weight (kg)/height squared (m2). BMI correlates with body fat (ADIPOSE TISSUE). Their relationship varies with age and gender. For adults, BMI falls into these categories: below 18.5 (underweight); 18.5-24.9 (normal); 25.0-29.9 (overweight); 30.0 and above (obese). (National Center for Health Statistics, Centers for Disease Control and Prevention)

**Light**: That portion of the electromagnetic spectrum in the visible, ultraviolet, and infrared range.

**Corneal Wavefront Aberration**: Asymmetries in the topography and refractive index of the corneal surface that affect visual acuity.

**Computational Biology**: A field of biology concerned with the development of techniques for the collection and manipulation of biological data, and the use of such data to make biological discoveries or predictions. This field encompasses all computational methods and theories for solving biological problems including manipulation of models and datasets.

**Mutation**: 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.

**Adipokines**: Polypeptides produced by the ADIPOCYTES. They include LEPTIN; ADIPONECTIN; RESISTIN; and many cytokines of the immune system, such as TUMOR NECROSIS FACTOR-ALPHA; INTERLEUKIN-6; and COMPLEMENT FACTOR D (also known as ADIPSIN). They have potent autocrine, paracrine, and endocrine functions.

**Risk Assessment**: The qualitative or quantitative estimation of the likelihood of adverse effects that may result from exposure to specified health hazards or from the absence of beneficial influences. (Last, Dictionary of Epidemiology, 1988)

**Electromyography**: Recording of the changes in electric potential of muscle by means of surface or needle electrodes.

**Biophysical Phenomena**: The physical characteristics and processes of biological systems.

**Cross-Over Studies**: Studies comparing two or more treatments or interventions in which the subjects or patients, upon completion of the course of one treatment, are switched to another. In the case of two treatments, A and B, half the subjects are randomly allocated to receive these in the order A, B and half to receive them in the order B, A. A criticism of this design is that effects of the first treatment may carry over into the period when the second is given. (Last, A Dictionary of Epidemiology, 2d ed)

**Biomechanical Phenomena**: The properties, processes, and behavior of biological systems under the action of mechanical forces.

**Facility Design and Construction**: Architecture, exterior and interior design, and construction of facilities other than hospitals, e.g., dental schools, medical schools, ambulatory care clinics, and specified units of health care facilities. The concept also includes architecture, design, and construction of specialized contained, controlled, or closed research environments including those of space labs and stations.

**Population Density**: Number of individuals in a population relative to space.

**Electrochemistry**: The study of chemical changes resulting from electrical action and electrical activity resulting from chemical changes.

**Urea**: A compound formed in the liver from ammonia produced by the deamination of amino acids. It is the principal end product of protein catabolism and constitutes about one half of the total urinary solids.

**Movement**: The act, process, or result of passing from one place or position to another. It differs from LOCOMOTION in that locomotion is restricted to the passing of the whole body from one place to another, while movement encompasses both locomotion but also a change of the position of the whole body or any of its parts. Movement may be used with reference to humans, vertebrate and invertebrate animals, and microorganisms. Differentiate also from MOTOR ACTIVITY, movement associated with behavior.

**Physical Phenomena**: The entities of matter and energy, and the processes, principles, properties, and relationships describing their nature and interactions.

**Pattern Recognition, Automated**: In INFORMATION RETRIEVAL, machine-sensing or identification of visible patterns (shapes, forms, and configurations). (Harrod's Librarians' Glossary, 7th ed)

**Seasons**: Divisions of the year according to some regularly recurrent phenomena usually astronomical or climatic. (From McGraw-Hill Dictionary of Scientific and Technical Terms, 6th ed)

**Pilot Projects**: Small-scale tests of methods and procedures to be used on a larger scale if the pilot study demonstrates that these methods and procedures can work.

**Quality of Life**: A generic concept reflecting concern with the modification and enhancement of life attributes, e.g., physical, political, moral and social environment; the overall condition of a human life.

**Brain**: The part of CENTRAL NERVOUS SYSTEM that is contained within the skull (CRANIUM). Arising from the NEURAL TUBE, the embryonic brain is comprised of three major parts including PROSENCEPHALON (the forebrain); MESENCEPHALON (the midbrain); and RHOMBENCEPHALON (the hindbrain). The developed brain consists of CEREBRUM; CEREBELLUM; and other structures in the BRAIN STEM.

**Spectroscopy, Fourier Transform Infrared**: A spectroscopic technique in which a range of wavelengths is presented simultaneously with an interferometer and the spectrum is mathematically derived from the pattern thus obtained.

**Scattering, Radiation**: The diversion of RADIATION (thermal, electromagnetic, or nuclear) from its original path as a result of interactions or collisions with atoms, molecules, or larger particles in the atmosphere or other media. (McGraw-Hill Dictionary of Scientific and Technical Terms, 6th ed)

**Phenotype**: The outward appearance of the individual. It is the product of interactions between genes, and between the GENOTYPE and the environment.

**Sensory Thresholds**: The minimum amount of stimulus energy necessary to elicit a sensory response.

**Martial Arts**: Activities in which participants learn self-defense mainly through the use of hand-to-hand combat. Judo involves throwing an opponent to the ground while karate (which includes kung fu and tae kwon do) involves kicking and punching an opponent.

**Numerical Analysis, Computer-Assisted**: Computer-assisted study of methods for obtaining useful quantitative solutions to problems that have been expressed mathematically.

**Survival Analysis**: A class of statistical procedures for estimating the survival function (function of time, starting with a population 100% well at a given time and providing the percentage of the population still well at later times). The survival analysis is then used for making inferences about the effects of treatments, prognostic factors, exposures, and other covariates on the function.

**Feeding Behavior**: Behavioral responses or sequences associated with eating including modes of feeding, rhythmic patterns of eating, and time intervals.

**Gastrointestinal Transit**: Passage of food (sometimes in the form of a test meal) through the gastrointestinal tract as measured in minutes or hours. The rate of passage through the intestine is an indicator of small bowel function.

**Imaging, Three-Dimensional**: The process of generating three-dimensional images by electronic, photographic, or other methods. For example, three-dimensional images can be generated by assembling multiple tomographic images with the aid of a computer, while photographic 3-D images (HOLOGRAPHY) can be made by exposing film to the interference pattern created when two laser light sources shine on an object.

**Psychometrics**: Assessment of psychological variables by the application of mathematical procedures.

**Recombination, Genetic**: Production of new arrangements of DNA by various mechanisms such as assortment and segregation, CROSSING OVER; GENE CONVERSION; GENETIC TRANSFORMATION; GENETIC CONJUGATION; GENETIC TRANSDUCTION; or mixed infection of viruses.

**Genetic Markers**: A phenotypically recognizable genetic trait which can be used to identify a genetic locus, a linkage group, or a recombination event.

## Sex differences in the effects of early neocortical injury on neuronal size distribution of the medial geniculate nucleus in the rat are mediated by perinatal gonadal steroids. (1/11846)

Freezing injury to the cortical plate of rats induces cerebrocortical microgyria and, in males but not females, a shift toward greater numbers of small neurons in the medial geniculate nucleus (MGN). The purpose of the current study was to examine a hormonal basis for this sex difference. Cross-sectional neuronal areas of the MGN were measured in male rats, untreated female rats and female rats treated perinatally with testosterone propionate, all of which had received either neonatal cortical freezing or sham injury. Both male and androgenized female rats with microgyria had significantly smaller MGN neurons when compared to their sham-operated counterparts, whereas untreated females with microgyria did not. These differences were also reflected in MGN neuronal size distribution: both male and androgenized female rats with microgyria had more small and fewer large neurons in their MGN in comparison to shams, while there was no difference in MGN neuronal size distribution between lesioned and sham females. These findings suggest that perinatal gonadal steroids mediate the sex difference in thalamic response to induction of microgyria in the rat cortex. (+info)## Natural history of dysplasia of the uterine cervix. (2/11846)

BACKGROUND: A historical cohort of Toronto (Ontario, Canada) women whose Pap smear histories were recorded at a major cytopathology laboratory provided the opportunity to study progression and regression of cervical dysplasia in an era (1962-1980) during which cervical squamous lesions were managed conservatively. METHODS: Actuarial and Cox's survival analyses were used to estimate the rates and relative risks of progression and regression of mild (cervical intraepithelial neoplasia 1 [CIN1]) and moderate (CIN2) dysplasias. In addition, more than 17,000 women with a history of Pap smears between 1970 and 1980 inclusive and who were diagnosed as having mild, moderate, or severe dysplasia were linked to the Ontario Cancer Registry for the outcome of any subsequent cervical cancers occurring through 1989. RESULTS: Both mild and moderate dysplasias were more likely to regress than to progress. The risk of progression from mild to severe dysplasia or worse was only 1% per year, but the risk of progression from moderate dysplasia was 16% within 2 years and 25% within 5 years. Most of the excess risk of cervical cancer for severe and moderate dysplasias occurred within 2 years of the initial dysplastic smear. After 2 years, in comparison with mild dysplasia, the relative risks for progression from severe or moderate dysplasia to cervical cancer in situ or worse was 4.2 (95% confidence interval [CI] = 3.0-5.7) and 2.5 (95% CI = 2.2-3.0), respectively. CONCLUSION: The risk of progression for moderate dysplasia was intermediate between the risks for mild and severe dysplasia; thus, the moderate category may represent a clinically useful distinction. The majority of untreated mild dysplasias were recorded as regressing to yield a normal smear within 2 years. (+info)## Low-dose combination therapy as first-line hypertension treatment for blacks and nonblacks. (3/11846)

To assess the efficacy and safety of bisoprolol/6.25-mg hydrochlorothiazide (HCTZ), amlodipine, and enalapril in black and nonblack patients, data from two comparative studies were pooled and subgroup analyses performed. Both studies had similar designs and included all three active treatments. The second study also included a placebo group. Subjects (n = 541) with a sitting diastolic blood pressure of 95-114 mmHg were titrated to achieve a diastolic blood pressure < or = 90 mmHg. The studies included 114 blacks and 427 nonblacks. Results of an intention-to-treat analysis of mean change from baseline after 12 weeks of treatment showed the following: 1) blood pressure was significantly lowered by all three active drugs compared with baseline or placebo; 2) in blacks, bisoprolol/6.25-mg HCTZ resulted in significantly greater reductions of systolic and diastolic blood pressure than enalapril or placebo, but was not significantly different from amlodipine; 3) in nonblacks, bisoprolol/6.25-mg HCTZ resulted in significantly greater reduction of diastolic blood pressure than amlodipine, enalapril, or placebo. The placebo-corrected change in blood pressure was greater for blacks than whites on the bisoprolol/6.25-mg HCTZ combination, but this was not statistically significant. Bisoprolol/6.25-mg HCTZ controlled diastolic blood pressure to < or = 90 mmHg in significantly more patients than enalapril or placebo in blacks and nonblacks. The difference in control rates was not significant versus amlodipine. The incidence of drug-related adverse events was similar between treatments; however, bisoprolol/6.25-mg HCTZ had a lower discontinuation rate due to lack of blood pressure control or adverse experiences in both blacks and nonblacks. (+info)## Extent and severity of atherosclerotic involvement of the aortic valve and root in familial hypercholesterolaemia. (4/11846)

OBJECTIVE: To compare the frequency of valvar and supravalvar aortic stenosis in homozygous and heterozygous familial hypercholesterolaemia (FH). DESIGN: Analysis of life time cholesterol exposure and prevalence of aortic atherosclerosis in 84 consecutive cases attending a lipid clinic. SETTING: A tertiary referral centre in London. PATIENTS: Outpatients with FH (six homozygous, 78 heterozygous). INTERVENTIONS: Maintenance of lipid lowering treatment. MAIN OUTCOME MEASURES: Calculated cholesterol x years score (CYS) and echocardiographic measurement of aortic root diameter, aortic valve thickness, and transaortic gradient. RESULTS: Four homozygotes with a mean (SD) CYS of 387 (124) mmol/1 x years had severe aortic stenosis (treatment started after seven years of age), whereas the other two had echocardiographic evidence of supravalvar thickening but no aortic valve stenosis (treatment started before three years of age). On multivariate analysis, mean transaortic gradient correlated significantly with CYS (mean = 523 (175) mmol/1 x years) in heterozygotes (p = 0.0001), but only two had severe aortic valve and root involvement. CONCLUSIONS: In patients with familial hypercholesterolaemia, aortic stenosis is common in homozygotes, and aortic root involvement is always present despite the lower CYS than in heterozygotes. It appears to be determined by short term exposure to high cholesterol concentrations in early life. Conversely, aortic root and valve involvement are rare in heterozygotes and occur only with severe, prolonged hypercholesterolaemia, possibly accelerating age related degenerative effects. (+info)## Amino acid composition of protein termini are biased in different manners. (5/11846)

An exhaustive statistical analysis of the amino acid sequences at the carboxyl (C) and amino (N) termini of proteins and of coding nucleic acid sequences at the 5' side of the stop codons was undertaken. At the N ends, Met and Ala residues are over-represented at the first (+1) position whereas at positions 2 and 5 Thr is preferred. These peculiarities at N-termini are most probably related to the mechanism of initiation of translation (for Met) and to the mechanisms governing the life-span of proteins via regulation of their degradation (for Ala and Thr). We assume that the C-terminal bias facilitates fixation of the C ends on the protein globule by a preference for charged and Cys residues. The terminal biases, a novel feature of protein structure, have to be taken into account when molecular evolution, three-dimensional structure, initiation and termination of translation, protein folding and life-span are concerned. In addition, the bias of protein termini composition is an important feature which should be considered in protein engineering experiments. (+info)## Prevalence of true vein graft aneurysms: implications for aneurysm pathogenesis. (6/11846)

BACKGROUND: Circumstantial evidence suggests that arterial aneurysms have a different cause than atherosclerosis and may form part of a generalized dilating diathesis. The aim of this study was to compare the rates of spontaneous aneurysm formation in vein grafts performed either for popliteal aneurysms or for occlusive disease. The hypothesis was that if arterial aneurysms form a part of a systemic process, then the rates of vein graft aneurysms should be higher for patients with popliteal aneurysms than for patients with lower limb ischemia caused by atherosclerosis. METHODS: Infrainguinal vein grafting procedures performed from 1990 to 1995 were entered into a prospective audit and graft surveillance program. Aneurysmal change was defined as a focal increase in the graft diameter of 1.5 cm or greater, excluding false aneurysms and dilatations after graft angioplasty. RESULTS: During the study period, 221 grafting procedures were performed in 200 patients with occlusive disease and 24 grafting procedures were performed in 21 patients with popliteal aneurysms. Graft surveillance revealed spontaneous aneurysm formation in 10 of the 24 bypass grafts (42%) for popliteal aneurysms but in only 4 of the 221 grafting procedures (2%) that were performed for chronic lower limb ischemia. CONCLUSION: This study provides further evidence that aneurysmal disease is a systemic process, and this finding has clinical implications for the treatment of popliteal aneurysms. (+info)## Cryoglobulinaemia and rheumatic manifestations in patients with hepatitis C virus infection. (7/11846)

OBJECTIVES: To investigate the association of cryoglobulinaemia and rheumatic manifestations in Korean patients with hepatitis C virus (HCV) infection. METHODS: Forty nine Korean patients with HCV infection were recruited. The prevalence, concentration, and type of cryoglobulin (by immunofixation), rheumatoid factor (RF), antinuclear antibody (ANA), and various rheumatological symptoms were investigated and HCV genotype was determined by polymerase chain reaction with genotype specific primer. RESULTS: The prevalence of cryoglobulin was 59% in Korean HCV patients and the concentration of cryoglobulin was 9.8 (7.9) g/l (mean (SD)). The type of cryoglobulinaemia was identified in 23 (80%) of 29 HCV patients with cryoglobulinaemia and they were all type III. There were no differences in age, sex, history of operation and transfusion, proportion of liver cirrhosis between the patients with cryoglobulinaemia and those without cryoglobulinaemia. The frequencies of RF and ANA were 14% and 3.4% respectively in HCV patients with cryoglobulinaemia. There was no difference in HCV genotype between the patients with cryoglobulinaemia and those without cryoglobulinaemia. Clinical features of HCV patients were as follows: arthralgia/arthritis (35%), cutaneous manifestation (37%), Raynaud's phenomenon (8%), paresthesia (44%), dry eyes (22%), dry mouth (10%), oral ulcer (33%), and abdominal pain (14%). However, these rheumatological symptoms did not differ between the two groups. CONCLUSION: Although the rheumatological symptoms were not different between HCV patients with and without cryoglobulinaemia, HCV patients showed various rheumatological manifestations. These result suggests that HCV infection could be included as one of the causes in patients with unexplained rheumatological symptoms. (+info)## Fetal tachycardias: management and outcome of 127 consecutive cases. (8/11846)

OBJECTIVE: To review the management and outcome of fetal tachycardia, and to determine the problems encountered with various treatment protocols. STUDY DESIGN: Retrospective analysis. SUBJECTS: 127 consecutive fetuses with a tachycardia presenting between 1980 and 1996 to a single tertiary centre for fetal cardiology. The median gestational age at presentation was 32 weeks (range 18 to 42). RESULTS: 105 fetuses had a supraventricular tachycardia and 22 had atrial flutter. Overall, 52 fetuses were hydropic and 75 non-hydropic. Prenatal control of the tachycardia was achieved in 83% of treated non-hydropic fetuses compared with 66% of the treated hydropic fetuses. Digoxin monotherapy converted most (62%) of the treated non-hydropic fetuses, and 96% survived through the neonatal period. First line drug treatment for hydropic fetuses was more diverse, including digoxin (n = 5), digoxin plus verapamil (n = 14), and flecainide (n = 27). The response rates to these drugs were 20%, 57%, and 59%, respectively, confirming that digoxin monotherapy is a poor choice for the hydropic fetus. Response to flecainide was faster than to the other drugs. Direct fetal treatment was used in four fetuses, of whom two survived. Overall, 73% (n = 38) of the hydropic fetuses survived. Postnatally, 4% of the non-hydropic group had ECG evidence of pre-excitation, compared with 16% of the hydropic group; 57% of non-hydropic fetuses were treated with long term anti-arrhythmics compared with 79% of hydropic fetuses. CONCLUSIONS: Non-hydropic fetuses with tachycardias have a very good prognosis with transplacental treatment. Most arrhythmias associated with fetal hydrops can be controlled with transplacental treatment, but the mortality in this group is 27%. At present, there is no ideal treatment protocol for these fetuses and a large prospective multicentre trial is required to optimise treatment of both hydropic and non-hydropic fetuses. (+info)Typically the

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**distribution**laws of statistics analogous to pearson's**chi**-**square**". Statistics: A Journal of Theoretical and ... Z. W. Birnbaum; I. Vincze (1973). "Limiting**Distributions**of Statistics Similar to Student's". Annals of Statistics. 1 (1973): ... Vincze, István (1996). "Cramér-Rao type inequality and a problem of mixture of**distributions**". Mathematical Institute, Slovak ... empirical**distribution**, Cramér-Rao inequality, and information theory. Considered by many, as an expert in theoretical and ...This test yields a Wald statistic which follows a

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- This applet demonstrates the Binomial distribution by simulating Galton's Board, dropping balls through a triangular array of nails. (causeweb.org)
- 5.2 Working with Probabilities: The Binomial Distribution. (wiley.com)
- function uses the binomial distribution. (delorie.com)
- A negative binomial distribution with n = 1 is a geometric distribution. (wikipedia.org)
- Examples of such univariate distributions are: Normal distribution, Poisson distribution, Binomial distribution (with common success probability), Negative binomial distribution (with common success probability), Gamma distribution(with common rate parameter), Chi-squared distribution, Cauchy distribution, Hyper-exponential distribution. (wikipedia.org)
- The binomial distribution, which describes the number of successes in a series of independent Yes/No experiments all with the same probability of success. (wikipedia.org)
- The beta negative binomial distribution The Boltzmann distribution, a discrete distribution important in statistical physics which describes the probabilities of the various discrete energy levels of a system in thermal equilibrium. (wikipedia.org)
- Special cases include: The Gibbs distribution The Maxwell-Boltzmann distribution The Borel distribution The extended negative binomial distribution The extended hypergeometric distribution The generalized log-series distribution The geometric distribution, a discrete distribution which describes the number of attempts needed to get the first success in a series of independent Bernoulli trials, or alternatively only the number of losses before the first success (i.e. one less). (wikipedia.org)
- The logarithmic (series) distribution The negative binomial distribution or Pascal distribution a generalization of the geometric distribution to the nth success. (wikipedia.org)
- Related to this distribution are a number of other distributions: the displaced Poisson, the hyper-Poisson, the general Poisson binomial and the Poisson type distributions. (wikipedia.org)
- Important and commonly encountered univariate probability distributions include the binomial distribution, the hypergeometric distribution, and the normal distribution. (wikipedia.org)
- citation needed] An exact binomial test can then be used, where b is compared to a binomial distribution with size parameter n = b + c and p = 0.5. (wikipedia.org)
- Fortunately, binomial distribution functions are readily available in common software packages and the McNemar mid-P test can easily be calculated. (wikipedia.org)
- Initial attempts to explain the spatial distribution of animals had been based on approaches like Bartlett's stochastic population models and the negative binomial distribution that could result from birth-death processes. (wikipedia.org)
- Or The actual probability distribution is given by a binomial distribution and the number of trials is sufficiently bigger than the number of successes one is asking about (see Related distributions). (wikipedia.org)
- conjugate to the Bernoulli distribution and binomial distribution Statistical inference is the process of drawing conclusions from data that are subject to random variation, for example, observational errors or sampling variation. (wikipedia.org)
- But T can also be used as a test statistic in one of two ways: the exact sampling distribution of T under the null hypothesis is the binomial distribution with parameters 0.5 and 100. (wikipedia.org)

- This new approximation exhibits remarkable accuracy even when the degrees of freedom of the F distribution are small. (scirp.org)
- distribution, where r is the degrees of freedom, which is the difference in the number of unconstrained parameters being estimated and the number of constrained parameters being estimated. (scirp.org)
- Table 5 provides the chi-square for the corresponding value of alpha and the number of degrees of freedom. (oreilly.com)
- Students compare the chi-square distribution to the standard normal distribution and determine how the Chi-Square distribution changes as they increase the degrees of freedom. (ti.com)
- As the degrees of freedom increase the distribution becomes less skewed and more symmetric. (ti.com)
- The chi-square distribution has one parameter k , the degrees of freedom. (symynet.com)
- If we wish to reject H o at the .05 level, we will determine if our value of chi square is greater than the critical value of chi square that cuts off the upper 5% of the distribution at our particular degrees of freedom value. (symynet.com)
- Degrees of freedom of the non-central chi-square distribution. (scilab.org)
- The degrees of freedom of the resulting chi-square distribution are equal to the number of variables that are summed. (gsu.edu)
- That is, a chi-square-distributed variable with d1 degrees of freedom can be added to one with d2 degrees of freedom to yield a chi-square-distributed variable with d1 + d2 degrees of freedom, as long as the two added variables are independent. (gsu.edu)
- Generate sample data of size 1000 from a noncentral chi-square distribution with degrees of freedom 8 and noncentrality parameter 3. (mathworks.com)
- Explain how the degrees of freedom affect a Chi-Square Distribution. (foxessays.com)
- Visualize how changes in degrees of freedom affect the shape of the chi square distribution. (rdrr.io)
- and the conditional distribution of Z given J = i is chi-squared with k + 2 i degrees of freedom. (wikipedia.org)
- Chi square distribution explains a variable with k degrees of liberty, dispersed like the amount of the squares of n independent random variables each which have a typical distribution with mean of absolutely no and variation of 1. (academicpaperwriter.com)
- You can quickly depend on our Chi-Square Distributions composing Help as we offer the very best services and these services are supplied to the students by our professionals who all hold master and specialized degrees or more. (academicpaperwriter.com)
- Pearson dealt first with the case in which the expected numbers m i are large enough known numbers in all cells assuming every x i may be taken as normally distributed , and reached the result that, in the limit as n becomes large, X 2 follows the χ 2 distribution with k − 1 degrees of freedom. (wikipedia.org)
- In probability theory and statistics, the chi-squared distribution (also chi-square or χ2-distribution) with k degrees of freedom is the distribution of a sum of the squares of k independent standard normal random variables. (wikipedia.org)
- The chi-squared distribution has one parameter: k - a positive integer that specifies the number of degrees of freedom (i. e. the number of Zi's). (wikipedia.org)
- It is also often defined as the distribution of a random variable whose reciprocal divided by its degrees of freedom is a chi-squared distribution. (wikipedia.org)
- If the null hypothesis had specified a single distribution, rather than requiring λ to be estimated, then the null distribution of the test statistic would be a chi-square distribution with 10 − 1 = 9 degrees of freedom. (wikipedia.org)
- The expected value of a chi-square random variable with 8 degrees of freedom is 8. (wikipedia.org)
- The distribution is therefore parametrised by the two quantities ν and τ2, referred to as the number of chi-squared degrees of freedom and the scaling parameter, respectively. (wikipedia.org)
- There are several methods to derive chi-squared distribution with 2 degrees of freedom. (wikipedia.org)
- A gamma (α, β) random variable with α = ν/2 and β = 2, is a chi-squared random variable with ν degrees of freedom. (wikipedia.org)
- A chi-squared distribution with 2 degrees of freedom is an exponential distribution with mean 2 and vice versa. (wikipedia.org)
- In statistics, the non-central chi-squared distribution with zero degrees of freedom can be used in testing the null hypothesis that a sample is from a uniform distribution on the interval (0, 1). (wikipedia.org)
- It is trivial that a "central" chi-square distribution with zero degrees of freedom concentrates all probability at zero. (wikipedia.org)
- Under the truth of the null hypothesis, the sampling distribution of the F ratio depends on the degrees of freedom for the numerator and the denominator. (wikipedia.org)
- The degrees of freedom are also commonly associated with the squared lengths (or "sum of squares" of the coordinates) of such vectors, and the parameters of chi-squared and other distributions that arise in associated statistical testing problems. (wikipedia.org)
- While introductory textbooks may introduce degrees of freedom as distribution parameters or through hypothesis testing, it is the underlying geometry that defines degrees of freedom, and is critical to a proper understanding of the concept. (wikipedia.org)
- While Gosset did not actually use the term 'degrees of freedom', he explained the concept in the course of developing what became known as Student's t-distribution. (wikipedia.org)
- The second residual vector is the least-squares projection onto the (n − 1)-dimensional orthogonal complement of this subspace, and has n − 1 degrees of freedom. (wikipedia.org)
- Siegel (1979) discusses the case k = 0 specifically (zero degrees of freedom), in which case the distribution has a discrete component at zero. (wikipedia.org)
- In order to determine the degrees of freedom of the chi-squared distribution, one takes the total number of observed frequencies and subtracts the number of estimated parameters. (wikipedia.org)
- The test statistic follows, approximately, a chi-square distribution with (k − c) degrees of freedom where k is the number of non-empty cells and c is the number of estimated parameters (including location and scale parameters and shape parameters) for the distribution. (wikipedia.org)
- Sum of squares (statistics) Squared deviations Errors and residuals in statistics Lack-of-fit sum of squares Degrees of freedom (statistics)#Sum of squares and degrees of freedom Chi-squared distribution#Applications Draper, N.R. (wikipedia.org)
- The most familiar examples are the Rayleigh distribution with chi distribution with 2 degrees of freedom, and the Maxwell distribution of (normalized) molecular speeds which is a chi distribution with 3 degrees of freedom (one for each spatial coordinate). (wikipedia.org)
- That is fortunate because it means that even though we do not know σ, we know the probability distribution of this quotient: it has a Student's t-distribution with n − 1 degrees of freedom. (wikipedia.org)
- Because R2 is the square of the norm of the standard bivariate normal variable (X, Y), it has the chi-squared distribution with two degrees of freedom. (wikipedia.org)
- In the special case of two degrees of freedom, the chi-squared distribution coincides with the exponential distribution, and the equation for R2 above is a simple way of generating the required exponential variate. (wikipedia.org)
- From this auxiliary regression, the explained sum of squares is retained, divided by two, and then becomes the test statistic for a chi-squared distribution with the degrees of freedom equal to the number of independent variables. (wikipedia.org)
- From the auxiliary regression, it retains the R-squared value which is then multiplied by the sample size, and then becomes the test statistic for a chi-squared distribution (and uses the same degrees of freedom). (wikipedia.org)
- Cochran's theorem states that the Qi are independent, and each Qi has a chi-squared distribution with ri degrees of freedom. (wikipedia.org)
- In statistics, the Wishart distribution is a generalization to multiple dimensions of the chi-squared distribution, or, in the case of non-integer degrees of freedom, of the gamma distribution. (wikipedia.org)
- If p = V = 1 then this distribution is a chi-squared distribution with n degrees of freedom. (wikipedia.org)
- Under the null hypothesis, this statistic has asymptotically the chi-squared distribution with the number of degrees of freedom equal to the rank of matrix Var(b0) − Var(b1). (wikipedia.org)
- This follows a chi-squared distribution, with degrees of freedom equal to P − 1, where P is the number of estimated parameters (in the auxiliary regression). (wikipedia.org)

- The normal, or Gaussian, distribution is one of the most familiar in statistics, endeared to statisticians by its simplicity and by virtue of the Central Limit Theorem (which states that a sample mean will follow an approximately normal distribution, if sample size is large enough, even if the data themselves are not normally distributed). (gsu.edu)
- Test statistics that follow a chi-squared distribution arise from an assumption of independent normally distributed data, which is valid in many cases due to the central limit theorem . (wikipedia.org)
- For these hypothesis tests, as the sample size, n, increases, the sampling distribution of the test statistic approaches the normal distribution (central limit theorem). (wikipedia.org)
- For large N, the distribution of the mean can be determined from the central limit theorem for directional statistics. (wikipedia.org)
- The normal distribution is useful because of the central limit theorem. (wikipedia.org)

- For example, the test statistic for testing equality of variances of two independently distributed normal distributions is distributed as an F distribution. (scirp.org)
- The chi-square test is a statistical test based on comparison of a test statistic to a chi-square distribution . (biology-online.org)
- Chi-square Test Statistic. (routledge.com)
- A chi-squared test , also written as χ 2 test , is any statistical hypothesis test where the sampling distribution of the test statistic is a chi-squared distribution when the null hypothesis is true. (wikipedia.org)
- Because the test statistic (such as t) is asymptotically normally distributed, provided the sample size is sufficiently large, the distribution used for hypothesis testing may be approximated by a normal distribution. (wikipedia.org)
- Thus, as the sample size for a hypothesis test increases, the distribution of the test statistic approaches a normal distribution, and the distribution of the square of the test statistic approaches a chi-squared distribution. (wikipedia.org)
- In certain chi-square tests, one rejects a null hypothesis about a population distribution if a specified test statistic is too large, when that statistic would have approximately a chi-square distribution if the null hypothesis is true. (wikipedia.org)
- In minimum chi-square estimation, one finds the values of parameters that make that test statistic as small as possible. (wikipedia.org)
- Among the consequences of its use is that the test statistic actually does have approximately a chi-square distribution when the sample size is large. (wikipedia.org)
- One might hope that the resulting test statistic would have approximately a chi-square distribution when the null hypothesis is true. (wikipedia.org)
- This result is used to justify using a normal distribution, or a chi square distribution (depending on how the test statistic is calculated), when conducting a hypothesis test. (wikipedia.org)
- In contexts where it is important to improve a distinction between the test statistic and its distribution, names similar to Pearson χ-squared test or statistic are used. (wikipedia.org)
- Whereas the central distribution describes how a test statistic is distributed when the difference tested is null, noncentral distributions describe the distribution of a test statistic when the null is false (alternative hypothesis). (wikipedia.org)
- Both the form of the Kolmogorov-Smirnov test statistic and its asymptotic distribution under the null hypothesis were published by Andrey Kolmogorov, while a table of the distribution was published by Nikolai Vasilyevich Smirnov. (wikipedia.org)
- Recurrence relations for the distribution of the test statistic in finite samples are available. (wikipedia.org)
- An important property of a test statistic is that its sampling distribution under the null hypothesis must be calculable, either exactly or approximately, which allows p-values to be calculated. (wikipedia.org)
- the value of T can be compared with its expected value under the null hypothesis of 50, and since the sample size is large a normal distribution can be used as an approximation to the sampling distribution either for T or for the revised test statistic T−50. (wikipedia.org)

- A gaussian approximation to the distribution of a definite quadratic form. (springer.com)
- Royen published this proof in an article with the title A simple proof of the Gaussian correlation conjecture extended to multivariate gamma distributions on arXiv and subsequently in the Far East Journal of Theoretical Statistics, a relatively unknown periodical based in Allahabad, India, for which Royen was at the time voluntarily working as a referee himself. (wikipedia.org)
- Percentiles can be determined by recognizing that the squared distance defined by two uncorrelated orthogonal Gaussian random variables (one for each axis) is chi-square distributed. (wikipedia.org)
- Support for Gaussian, Student's t and exponential power distribution (GED) distributed innovations/shocks. (wikipedia.org)
- In probability theory, the normal (or Gaussian) distribution is a very common continuous probability distribution. (wikipedia.org)
- A random variable with a Gaussian distribution is said to be normally distributed and is called a normal deviate. (wikipedia.org)
- The random variable associated with this distribution comes about as the ratio of two Gaussian (normal) distributed variables with zero mean. (wikipedia.org)
- Two distributions often used in test-statistics, the t-distribution and the F-distribution, are also ratio distributions: The t-distributed random variable is the ratio of a Gaussian random variable divided by an independent chi-distributed random variable (i.e., the square root of a chi-squared distribution), while the F-distributed random variable is the ratio of two independent chi-squared distributed random variables. (wikipedia.org)
- When X and Y are independent and have a Gaussian distribution with zero mean, the form of their ratio distribution is fairly simple: It is a Cauchy distribution. (wikipedia.org)
- measles epidemiology HIV epidemiology, the geographic clustering of childhood leukemia blood flow heterogeneity the genomic distributions of single-nucleotide polymorphisms (SNPs) gene structures in number theory with sequential values of the Mertens function from the eigenvalue deviations of Gaussian orthogonal and unitary ensembles of random matrix theory The first use of a double log-log plot was by Reynolds in 1879 on thermal aerodynamics. (wikipedia.org)
- As λ tends to infinity, the inverse Gaussian distribution becomes more like a normal (Gaussian) distribution. (wikipedia.org)
- The inverse Gaussian distribution has several properties analogous to a Gaussian distribution. (wikipedia.org)
- The name can be misleading: it is an "inverse" only in that, while the Gaussian describes a Brownian Motion's level at a fixed time, the inverse Gaussian describes the distribution of the time a Brownian Motion with positive drift takes to reach a fixed positive level. (wikipedia.org)
- Han-era Chinese advancements in mathematics include the discovery of square roots, cube roots, the Pythagorean theorem, Gaussian elimination, the Horner scheme, improved calculations of pi, and negative numbers. (wikipedia.org)

- From DCDFLIB: Library of Fortran Routines for Cumulative Distribution Functions, Inverses, and Other Parameters (February, 1994) Barry W. Brown, James Lovato and Kathy Russell. (scilab.org)
- On the bad side, normal distributions increase the likelihood that the parameters of statistical models will not be identified , because there will be relatively few pieces of distinct information--fewer "knowns"--available for this purpose ( Bekker, Merckens and Wansbeek, 1994 ). (gsu.edu)
- Estimate the parameters of the noncentral chi-square distribution from the sample data. (mathworks.com)
- Be able to estimate parameters of standard distributions following the Maximum Likelihood approach. (york.ac.uk)
- Be able to derive a confidence interval, exact and/or approximate, for parameters of probability distributions. (york.ac.uk)
- Understand the theoretical framework of linear regression models: standard model assumptions, Least Squares estimators for the model parameters and their properties, inference techniques for the model parameters. (york.ac.uk)
- The arguments to the algebraic functions are the value of the random variable first, then whatever other parameters define the distribution. (delorie.com)
- Let z have a multivariate normal distribution with zero mean and covariance matrix B, then the value of the quadratic form X = zTAz, where A is a matrix, has a generalised chi-squared distribution with parameters A and B. Note that there is some redundancy in this formulation, as for any matrix C, the distribution with parameters CTAC and B is identical to the distribution with parameters A and CBCT. (wikipedia.org)
- Computer code for evaluating the cumulative distribution function of the generalized chi-squared distribution has been published, but some preliminary manipulation of the parameters of the distribution is usually necessary. (wikipedia.org)
- The following techniques of distribution fitting exist: Parametric methods, by which the parameters of the distribution are calculated from the data series. (wikipedia.org)
- In probability and statistics, the generalized beta distribution is a continuous probability distribution with five parameters, including more than thirty named distributions as limiting or special cases. (wikipedia.org)
- As used in describing simple linear regression analysis, one assumption of the fitted model (to ensure that the least-squares estimators are each a best linear unbiased estimator of the respective population parameters, by the Gauss-Markov theorem) is that the standard deviations of the error terms are constant and do not depend on the x-value. (wikipedia.org)
- The original concept of CEP was based on a circular bivariate normal distribution (CBN) with CEP as a parameter of the CBN just as μ and σ are parameters of the normal distribution. (wikipedia.org)
- For a test of goodness-of-fit, this is essentially the number of categories reduced by the number of parameters of the fitted distribution. (wikipedia.org)
- The following distributions are non-log-concave for all parameters: The Student's t-distribution. (wikipedia.org)
- Noncentrality parameters are parameters of families of probability distributions that are related to other "central" families of distributions. (wikipedia.org)
- Noncentrality parameters are used in the following distributions: Noncentral t-distribution Noncentral chi-squared distribution Noncentral chi-distribution Noncentral F-distribution Noncentral beta distribution In general, noncentrality parameters occur in distributions that are transformations of a normal distribution. (wikipedia.org)
- However, there are extended versions of these distributions which have two noncentrality parameters: the doubly noncentral beta distribution, the doubly noncentral F distribution and the doubly noncentral t distribution. (wikipedia.org)
- The noncentrality parameter of the t-distribution may be negative or positive while the noncentral parameters of the other three distributions must be greater than zero. (wikipedia.org)
- In statistics, ordinary least squares (OLS) or linear least squares is a method for estimating the unknown parameters in a linear regression model. (wikipedia.org)
- OLS chooses the parameters of a linear function of a set of explanatory variables by minimizing the sum of the squares of the differences between the observed dependent variable (values of the variable being predicted) in the given dataset and those predicted by the linear function. (wikipedia.org)
- In statistics and mathematics, linear least squares is an approach to fitting a mathematical or statistical model to data in cases where the idealized value provided by the model for any data point is expressed linearly in terms of the unknown parameters of the model. (wikipedia.org)
- The approach is called linear least squares since the assumed function is linear in the parameters to be estimated. (wikipedia.org)
- Linear least squares problems are convex and have a closed-form solution that is unique, provided that the number of data points used for fitting equals or exceeds the number of unknown parameters, except in special degenerate situations. (wikipedia.org)
- If a random variable X has an F-distribution with parameters d1 and d2, we write X ~ F(d1, d2). (wikipedia.org)
- In many applications, the parameters d1 and d2 are positive integers, but the distribution is well-defined for positive real values of these parameters. (wikipedia.org)

- This applet demonstrates the Normal approximation to the Poisson Distribution. (causeweb.org)
- The Poisson distribution is shown in blue, and the Normal distribution is shown in red. (causeweb.org)
- From this representation, the noncentral chi-squared distribution is seen to be a Poisson-weighted mixture of central chi-squared distributions. (wikipedia.org)
- One could apply Pearson's chi-square test of whether the population distribution is a Poisson distribution with expected value 3.3. (wikipedia.org)
- The discrete compound Poisson distribution The parabolic fractal distribution The Poisson distribution, which describes a very large number of individually unlikely events that happen in a certain time interval. (wikipedia.org)
- The Conway-Maxwell-Poisson distribution, a two-parameter extension of the Poisson distribution with an adjustable rate of decay. (wikipedia.org)
- The Zero-truncated Poisson distribution, for processes in which zero counts are not observed The Polya-Eggenberger distribution The Skellam distribution, the distribution of the difference between two independent Poisson-distributed random variables. (wikipedia.org)
- Experience shows n must be quite large, say n ≥ 2¹⁸, for comparing the results to the Poisson distribution with that mean. (wikipedia.org)
- This test uses n = 2²⁴ and m = 2⁹, so that the underlying distribution for j is taken to be Poisson with λ = 2²⁷÷2²⁶ = 2. (wikipedia.org)
- in English often rendered /ˈpwɑːsɒn/), named after French mathematician Siméon Denis Poisson, 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 rate and independently of the time since the last event. (wikipedia.org)
- The Poisson distribution can also be used for the number of events in other specified intervals such as distance, area or volume. (wikipedia.org)
- If receiving any particular piece of mail does not affect the arrival times of future pieces of mail, i.e., if pieces of mail from a wide range of sources arrive independently of one another, then a reasonable assumption is that the number of pieces of mail received in a day obeys a Poisson distribution. (wikipedia.org)
- The Poisson distribution is popular for modelling the number of times an event occurs in an interval of time or space. (wikipedia.org)
- The Poisson distribution may be useful to model events such as The number of meteorites greater than 1 meter diameter that strike Earth in a year The number of patients arriving in an emergency room between 10 and 11 pm The Poisson distribution is an appropriate model if the following assumptions are true. (wikipedia.org)
- If these conditions are true, then k is a Poisson random variable, and the distribution of k is a Poisson distribution. (wikipedia.org)
- This equation is the probability mass function (PMF) for a Poisson distribution. (wikipedia.org)

- In this paper, a simple chi-square approximation for the cumulative distribution of the F -distribution is obtained via an adjusted log-likelihood ratio statistic. (scirp.org)
- Johnson and Kotz give a comprehensive review on the approximations to the cumulative distribution function (cdf) of the F distribution. (scirp.org)
- They find the critical values using a chart and then confirm the area between the critical values and in each tail using the cumulative Chi-Square command. (ti.com)
- Formula 26.4.25 of Abramowitz and Stegun, Handbook of Mathematical Functions (1966) is used to compute the cumulative distribution function. (scilab.org)
- Define a custom probability density and cumulative distribution function. (mathworks.com)
- Cumulative Probability Distributions A cumulative probability refers to the probability that the value of a random variable falls within a specified range. (slideplayer.com)
- 1) = P(X = 0) + P(X = 1) = = 0.75 Like a probability distribution, a cumulative probability distribution can be represented by a table or an equation. (slideplayer.com)
- A probability distribution is called discrete if its cumulative distribution function only increases in jumps. (mcgill.ca)
- If X has cumulative distribution function FX, then the inverse of the cumulative distribution F−1 X(X) is a standard uniform (0,1) random variable If X is a normal (μ, σ2) random variable then eX is a lognormal (μ, σ2) random variable. (wikipedia.org)
- The latter can be seen by calculating the cumulative distribution function for s in the interval (0, 1). (wikipedia.org)
- the probability that the outcome lies in a given interval can be computed by taking the difference between the values of the cumulative distribution function at the endpoints of the interval. (wikipedia.org)
- The cumulative distribution function is the antiderivative of the probability density function provided that the latter function exists. (wikipedia.org)
- The following terms are used for non-cumulative probability distribution functions: Frequency distribution: A frequency distribution is a table that displays the frequency of various outcomes in a sample. (wikipedia.org)
- The parametric methods are: method of moments method of L-moments Maximum likelihood method Regression method, using a transformation of the cumulative distribution function so that a linear relation is found between the cumulative probability and the values of the data, which may also need to be transformed, depending on the selected probability distribution. (wikipedia.org)
- Skewed distributions can be inverted (or mirrored) by replacing in the mathematical expression of the cumulative distribution function (F) by its complement: F'=1-F, obtaining the complementary distribution function (also called survival function) that gives a mirror image. (wikipedia.org)
- Note that the cumulative distribution function (CDF) of all log-concave distributions is also log-concave. (wikipedia.org)
- The following are among the properties of log-concave distributions: If a density is log-concave, so is its cumulative distribution function (CDF). (wikipedia.org)
- The Kolmogorov-Smirnov statistic quantifies a distance between the empirical distribution function of the sample and the cumulative distribution function of the reference distribution, or between the empirical distribution functions of two samples. (wikipedia.org)
- The two-sample K-S test is one of the most useful and general nonparametric methods for comparing two samples, as it is sensitive to differences in both location and shape of the empirical cumulative distribution functions of the two samples. (wikipedia.org)

- Unlike more widely known distributions such as the normal distribution and the exponential distribution, the chi-squared distribution is not as often applied in the direct modeling of natural phenomena. (wikipedia.org)

- Much of the distributional theory that underlies SEM today is built upon a handful of continuous statistical distributions--some well known, and some less so. (gsu.edu)
- The normal distribution also lies at the root of many other continuous statistical distributions. (gsu.edu)
- Monte Carlo and Statistical Distributions. (routledge.com)
- Organized for easy navigation and quick reference, this book is an invaluable resource for investors, data analysts, or anyone working with statistical distributions on a regular basis. (wiley.com)
- Distance between statistical distributions had been addressed in 1936 by Bhattacharyya's mentor, Mahalanobis, who proposed the D2 metric, now known as Mahalanobis distance. (wikipedia.org)

- Bentler's EQS package includes estimators specifically designed to be appropriate for elliptical distributions. (gsu.edu)
- Unbiased estimators of multivariate discrete distributions and chi-square goodness-of-fit test. (eudml.org)
- BAN estimator}, language = {eng}, number = {3}, pages = {301-326}, title = {Unbiased estimators of multivariate discrete distributions and chi-square goodness-of-fit test. (eudml.org)
- The jackknife is consistent for the sample means, sample variances, central and non-central t-statistics (with possibly non-normal populations), sample coefficient of variation, maximum likelihood estimators, least squares estimators, correlation coefficients and regression coefficients. (wikipedia.org)

- Surveys basic statistical methods used in the genetics and epidemiology literature, including maximum likelihood and least squares. (wiley.com)
- Minimum Chi-Square, Not Maximum Likelihood! (wikipedia.org)
- Maximum likelihood estimations using individual, grouped, or top-coded data are easily performed with these distributions. (wikipedia.org)
- Residual sum of squares Response bias Response rate (survey) Response surface methodology Response variable Restricted maximum likelihood Restricted randomization Reversible-jump Markov chain Monte Carlo Reversible dynamics Rind et al. (wikipedia.org)

- Continuous univariate distributions , vol. 2 of Wiley Series in Probability and Mathematical Statistics: Applied Probability and Statistics . (springer.com)
- The chi-square distribution is a univariate distribution which results when univariate-normal variables are squared, and possibly summed. (gsu.edu)
- Suppose there is a series of observations from a univariate distribution and we want to estimate the mean of that distribution (the so-called location model). (wikipedia.org)
- A probability distribution whose sample space is the set of real numbers is called univariate, while a distribution whose sample space is a vector space is called multivariate. (wikipedia.org)
- A probability distribution can either be univariate or multivariate. (wikipedia.org)

- In statistics, the residual sum of squares (RSS), also known as the sum of squared residuals (SSR) or the sum of squared errors of prediction (SSE), is the sum of the squares of residuals (deviations predicted from actual empirical values of data). (wikipedia.org)
- In general, total sum of squares = explained sum of squares + residual sum of squares. (wikipedia.org)
- To have a lack-of-fit sum of squares that differs from the residual sum of squares, one must observe more than one y-value for each of one or more of the x-values. (wikipedia.org)
- Although it is not necessary for the Koenker-Bassett test, the Breusch-Pagan test requires that the squared residuals also be divided by the residual sum of squares divided by the sample size. (wikipedia.org)

- The concept of the probability distribution and the random variables which they describe underlies the mathematical discipline of probability theory , and the science of statistics . (mcgill.ca)
- In probability theory and statistics, the specific name generalized chi-squared distribution (also generalized chi-square distribution) arises in relation to one particular family of variants of the chi-squared distribution. (wikipedia.org)
- In probability theory and statistics, there are several relationships among probability distributions. (wikipedia.org)
- In probability theory and statistics, the chi distribution is a continuous probability distribution. (wikipedia.org)
- In probability theory and statistics, a probability distribution is a mathematical function that, stated in simple terms, can be thought of as providing the probabilities of occurrence of different possible outcomes in an experiment. (wikipedia.org)
- In probability theory and directional statistics, a circular uniform distribution is a probability distribution on the unit circle whose density is uniform for all angles. (wikipedia.org)
- In probability theory, the Rice distribution, Rician distribution or Ricean distribution is the probability distribution of the magnitude of a circular bivariate normal random variable with potentially non-zero mean. (wikipedia.org)

- Sampling Distributions. (routledge.com)
- Sampling Distributions under Normality. (wikipedia.org)

- This page provides a table of Chi-square distribution probabilities with degress of freedom 1-45. (causeweb.org)
- This page provides a table of F distribution probabilities for alpha = 0.10, 0.05, 0.025, and 0.01. (causeweb.org)
- these two values and two probabilities make up the probability distribution of the single coin flipping event. (mcgill.ca)
- an approach based on the chi-square distribution for combining the individual word probabilities into a combined probability (actually a pair of probabilities-see below) representing an e-mail. (wikipedia.org)
- The uniform distribution on the interval [0, is decomposable, since it is the sum of the Bernoulli variable that assumes 0 or 1/2 with equal probabilities and the uniform distribution on [0, 1/ (wikipedia.org)
- In more technical terms, the probability distribution is a description of a random phenomenon in terms of the probabilities of events. (wikipedia.org)
- A discrete probability distribution (applicable to the scenarios where the set of possible outcomes is discrete, such as a coin toss or a roll of dice) can be encoded by a discrete list of the probabilities of the outcomes, known as a probability mass function. (wikipedia.org)
- a multivariate distribution (a joint probability distribution) gives the probabilities of a random vector-a list of two or more random variables-taking on various combinations of values. (wikipedia.org)
- The numerical method may consist of assuming a range of p values, then applying the distribution fitting procedure repeatedly for all the assumed p values, and finally selecting the value of p for which the sum of squares of deviations of calculated probabilities from measured frequencies (chi square) is minimum, as is done in CumFreq. (wikipedia.org)
- The quantity X has the same distribution in Bayesian statistics, if an uninformative rescaling-invariant Jeffreys prior is taken for the prior probabilities of σ12 and σ22. (wikipedia.org)

- In classical statistics, there are three distributions often used in hypothesis testing: F and Chi-square distributions used in comparing variances and t distributions in comparing means. (thefreedictionary.com)
- The chi-square distribution is a special case of the gamma distribution and is one of the most widely used probability distributions in inferential statistics, e. g., in hypothesis testing or in construction of confidence intervals. (wikipedia.org)
- The chi-squared distribution is used primarily in hypothesis testing. (wikipedia.org)
- These include hypothesis testing, the partitioning of sums of squares, experimental techniques and the additive model. (wikipedia.org)
- Conversely, a "large" R2 (scaled by the sample size so that it follows the chi-squared distribution) counts against the hypothesis of homoskedasticity. (wikipedia.org)

- The functions in this section compute various probability distributions. (delorie.com)
- Treat the mean for each group as a score, and compute the variability (again, the sum of squares) of those three scores. (wikipedia.org)
- Further analyses of quantile-normalized data may then assume that distribution to compute significance values. (wikipedia.org)

- The method of least squares had been introduced into geodesy by Gauss and Helmert wrote a fine book on least squares (1872, with a second edition in 1907) in this tradition, which became a standard text. (wikipedia.org)

- On some sets of sufficient conditions leading to the normal bivariate distribution", Sankhya, 6 (1943) 399 - 406. (wikipedia.org)
- The radius around the true mean in a bivariate normal random variable, re-written in polar coordinates (radius and angle), follows a Hoyt distribution. (wikipedia.org)

- continuous distribution describes events over a continuous range, where the probability of a specific outcome is zero. (mcgill.ca)
- It represents a discrete probability distribution concentrated at 0 - a degenerate distribution - but the notation treats it as if it were a continuous distribution. (wikipedia.org)

- Does the sample represent the theoretical distribution? (physicsforums.com)
- That would depend on what theoretical distribution was stated in the problem. (physicsforums.com)
- Chi square distribution is a theoretical likelihood distribution in inferential data. (academicpaperwriter.com)
- Where necessary, the author provides basic theoretical explanations for distributions and background information regarding formulas. (wiley.com)
- Probability and Statistical Inference 1 (Autumn) will give students a theoretical and mathematically formal framework for joint and conditional distributions of random variables and for studying the asymptotic behaviour of sequences of random variables. (york.ac.uk)
- This is the theoretical distribution model for a balanced coin, an unbiased die, a casino roulette, or the first card of a well-shuffled deck. (wikipedia.org)

- F distribution is one of the most frequently used distributions in statistics. (scirp.org)
- Information about and tables for the chi-square distribution can be found in any elementary statistics text. (thefreedictionary.com)
- Browse other questions tagged probability statistics probability-distributions random-variables covariance or ask your own question . (stackexchange.com)
- Presenters: Nouruddin Boojhawoonah & Poonam Gopaul Notes reffered from statistics tutorial: Probability distribution. (slideplayer.com)
- This help page describes the probability distributions provided in the Statistics package, how to construct random variables using these distributions and the functions that are typically used in conjunction with these distributions. (maplesoft.com)
- Quantitative Methods in Linguistics offers a practical introduction to statistics and quantitative analysis with data sets drawn from the field and coverage of phonetics, psycholinguistics, sociolinguistics, historical linguistics, and syntax, as well as probability distribution and quantitative methods. (wiley.com)
- István Vincze ((1912-02-26)February 26, 1912 - (1999-04-18)April 18, 1999 ) was a Hungarian mathematician, known for his contributions to number theory, non-parametric statistics, empirical distribution, Cramér-Rao inequality, and information theory. (wikipedia.org)
- In probability and statistics, the inverse-chi-squared distribution (or inverted-chi-square distribution) is a continuous probability distribution of a positive-valued random variable. (wikipedia.org)
- In statistics, minimum chi-square estimation is a method of estimation of unobserved quantities based on observed data. (wikipedia.org)
- He made fundamental contributions to multivariate statistics, particularly for his measure of similarity between two multinomial distributions, known as the Bhattacharya coefficient, based on which he defined a metric, the Bhattacharya distance. (wikipedia.org)
- The skew elliptical distribution The Yule-Simon distribution The zeta distribution has uses in applied statistics and statistical mechanics, and perhaps may be of interest to number theorists. (wikipedia.org)
- In statistics, the multivariate t-distribution (or multivariate Student distribution) is a multivariate probability distribution. (wikipedia.org)
- The distribution (function) stands for an average number, as in all three kinds of statistics (Maxwell-Boltzmann, Bose-Einstein, Fermi-Dirac). (wikipedia.org)
- In statistics, the t-distribution was first derived as a posterior distribution in 1876 by Helmert and Lüroth. (wikipedia.org)
- 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)
- These distributions are of great importance in the estimation of covariance matrices in multivariate statistics. (wikipedia.org)
- In statistics, the Kolmogorov-Smirnov test (K-S test or KS test) is a nonparametric test of the equality of continuous, one-dimensional probability distributions that can be used to compare a sample with a reference probability distribution (one-sample K-S test), or to compare two samples (two-sample K-S test). (wikipedia.org)
- The following are some of the important topics in mathematical statistics: A probability distribution assigns a probability to each measurable subset of the possible outcomes of a random experiment, survey, or procedure of statistical inference. (wikipedia.org)
- Some informative descriptive statistics, such as the sample range, do not make good test statistics since it is difficult to determine their sampling distribution. (wikipedia.org)

- It also initiated much study of the contributions to sums of squares. (wikipedia.org)
- Cochran's theorem shows that the terms in a decomposition of a sum of squares of normal random variables into sums of squares of linear combinations of these variables always have independent chi-squared distributions. (wikipedia.org)

- Subsequently, Bhattacharya defined a cosine metric for distance between distributions, in a Calcutta Mathematical Society paper in 1943, expanding on some of the results in another paper in Sankhya in 1947. (wikipedia.org)
- Minimum distance estimation (MDE) is a statistical method for fitting a mathematical model to data, usually the empirical distribution. (wikipedia.org)
- Putting this on a mathematical basis, the ellipsoid that best represents the set's probability distribution can be estimated by building the covariance matrix of the samples. (wikipedia.org)

- The inverse-chi-squared distribution (or inverted-chi-square distribution ) is the probability distribution of a random variable whose multiplicative inverse (reciprocal) has a chi-squared distribution. (wikipedia.org)
- Both definitions are special cases of the scaled-inverse-chi-squared distribution. (wikipedia.org)
- Also, the scale inverse chi-squared distribution is presented as the distribution for the inverse of the mean of ν squared deviates, rather than the inverse of their sum. (wikipedia.org)
- 1995/2004) argue that the inverse chi-squared parametrisation is more intuitive. (wikipedia.org)

- The oldest of these tests are used to detect whether two or more population distributions differ from one another. (biology-online.org)
- Population Distributions. (routledge.com)
- Taylor's law has also been applied to assess the time dependent changes of population distributions. (wikipedia.org)

- as the chi square distribution is drawn. (rdrr.io)
- This might not be true even if the error term is assumed to be drawn from identical distributions. (wikipedia.org)
- Statisticians often contemplate a parameterized family of probability distributions, any member of which could be the distribution of some measurable aspect of each member of a population, from which a sample is drawn randomly. (wikipedia.org)

- Data were analyzed using paired Wilcoxon signed-rank tests, Spearman rank correlation coefficients, and Fischer's exact chi-square tests (alpha = 0.05) where appropriate. (nih.gov)

- Probability Distributions An example will make clear the relationship between random variables and probability distributions. (slideplayer.com)
- Be able to apply various limit theorems to prove convergence in probability or in distribution of a sequence of random variables. (york.ac.uk)
- The distribution of the sum of independent random variables is called the convolution of the primal distribution. (wikipedia.org)
- The sum of gamma (ni, β) random variables has a gamma (Σni, β) distribution. (wikipedia.org)
- To see, this, suppose U and V are independent random variables and U + V has this probability distribution. (wikipedia.org)
- A sum of indecomposable random variables is necessarily decomposable (as it is a sum), and in fact may a fortiori be an infinitely divisible distribution (not just decomposable as the given sum). (wikipedia.org)
- To define probability distributions for the simplest cases, one needs to distinguish between discrete and continuous random variables. (wikipedia.org)
- A ratio distribution (or quotient distribution) is a probability distribution constructed as the distribution of the ratio of random variables having two other known distributions. (wikipedia.org)
- The ratio is one type of algebra for random variables: Related to the ratio distribution are the product distribution, sum distribution and difference distribution. (wikipedia.org)
- Many of these distributions are described in Melvin D. Springer's book from 1979 The Algebra of Random Variables. (wikipedia.org)
- and experiments with sample spaces encoded by continuous random variables, where the distribution can be specified by a probability density function. (wikipedia.org)

- This probability distribution is called the uniform distribution. (slideplayer.com)
- Uniform Distribution. (slideplayer.com)
- Thus, we have a uniform distribution. (slideplayer.com)
- The discrete uniform distribution, where all elements of a finite set are equally likely. (wikipedia.org)
- The continuous uniform distribution or rectangular distribution on [a,b], where all points in a finite interval are equally likely. (wikipedia.org)
- The basic form as given by Box and Muller takes two samples from the uniform distribution on the interval [0, and maps them to two standard, normally distributed samples. (wikipedia.org)
- The sample mean for the circular uniform distribution will be concentrated about zero, becoming more concentrated as N increases. (wikipedia.org)
- The uniform distribution over any convex set. (wikipedia.org)