statistics Statistics (from German language, German: ''wikt:Statistik#German, Statistik'', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of ...

, a univariate distribution is a

probability distribution In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment. It is a mathematical description of a random phenomenon i ...

of only one

random variable A random variable (also called random quantity, aleatory variable, or stochastic variable) is a mathematical formalization of a quantity or object which depends on random events. It is a mapping or a function from possible outcomes (e.g., the po ...

. This is in contrast to a

multivariate distribution Given two random variables that are defined on the same probability space, the joint probability distribution is the corresponding probability distribution on all possible pairs of outputs. The joint distribution can just as well be considered ...

, the

of a

random vector In probability, and statistics, a multivariate random variable or random vector is a list of mathematical variables each of whose value is unknown, either because the value has not yet occurred or because there is imperfect knowledge of its value ...

(consisting of multiple random variables).

Examples

One of the simplest examples of a discrete univariate distribution is the discrete uniform distribution, where all elements of a finite set are equally likely. It is the probability model for the outcomes of tossing a fair coin, rolling a fair die, etc. The univariate

continuous uniform distribution In probability theory and statistics, the continuous uniform distribution or rectangular distribution is a family of symmetric probability distributions. The distribution describes an experiment where there is an arbitrary outcome that lies betw ...

on an interval 'a'', ''b''has the property that all sub-intervals of the same length are equally likely. Binomial Distribution

Other examples of discrete univariate distributions include the

binomial Binomial may refer to: In mathematics *Binomial (polynomial), a polynomial with two terms * Binomial coefficient, numbers appearing in the expansions of powers of binomials *Binomial QMF, a perfect-reconstruction orthogonal wavelet decomposition ...

, geometric,

negative binomial In probability theory and statistics, the negative binomial distribution is a discrete probability distribution that models the number of failures in a sequence of independent and identically distributed Bernoulli trials before a specified (non-r ...

, and

Poisson distribution In probability theory and statistics, the Poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known co ...

s.Johnson, N.L., Kemp, A.W., and Kotz, S. (2005) Discrete Univariate Distributions, 3rd Edition, Wiley, . At least 750 univariate discrete distributions have been reported in the literature.Wimmer G, Altmann G (1999) Thesaurus of univariate discrete probability distributions. STAMM Verlag GmbH Essen, 1st ed XXVII Examples of commonly applied continuous univariate distributionsJohnson N.L., Kotz S, Balakrishnan N. (1994) Continuous Univariate Distributions Vol 1. Wiley Series in Probability and Statistics. include the

normal distribution In statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is : f(x) = \frac e^ The parameter \mu ...

Student's t distribution In probability and statistics, Student's ''t''-distribution (or simply the ''t''-distribution) is any member of a family of continuous probability distributions that arise when estimating the mean of a normally distributed population in situa ...

chisquare distribution In probability theory and statistics, the chi-squared distribution (also chi-square or \chi^2-distribution) with k degrees of freedom is the distribution of a sum of the squares of k independent standard normal random variables. The chi-squa ...

F distribution In probability theory and statistics, the ''F''-distribution or F-ratio, also known as Snedecor's ''F'' distribution or the Fisher–Snedecor distribution (after Ronald Fisher and George W. Snedecor) is a continuous probability distribution t ...

exponential Exponential may refer to any of several mathematical topics related to exponentiation, including: *Exponential function, also: **Matrix exponential, the matrix analogue to the above * Exponential decay, decrease at a rate proportional to value *Exp ...

and

gamma Gamma (uppercase , lowercase ; ''gámma'') is the third letter of the Greek alphabet. In the system of Greek numerals it has a value of 3. In Ancient Greek, the letter gamma represented a voiced velar stop . In Modern Greek, this letter re ...

distributions.

Examples

See also

References

Further reading