statistics Statistics (from German language, German: ', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a s ...

, a univariate distribution is a

probability distribution In probability theory and statistics, a probability distribution is a Function (mathematics), function that gives the probabilities of occurrence of possible events for an Experiment (probability theory), experiment. It is a mathematical descri ...

of only one

random variable A random variable (also called random quantity, aleatory variable, or stochastic variable) is a Mathematics, mathematical formalization of a quantity or object which depends on randomness, random events. The term 'random variable' in its mathema ...

. This is in contrast to a multivariate distribution, the

of a

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

(consisting of multiple random variables).

Examples

One of the simplest examples of a discrete univariate distribution is the

discrete uniform distribution In probability theory and statistics, the discrete uniform distribution is a symmetric probability distribution wherein each of some finite whole number ''n'' of outcome values are equally likely to be observed. Thus every one of the ''n'' out ...

, 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 distributions or rectangular distributions are a family of symmetric probability distributions. Such a distribution describes an experiment where there is an arbitrary outcome that li ...

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

Other examples of discrete univariate distributions include the binomial, geometric,

negative binomial In probability theory and statistics, the negative binomial distribution, also called a Pascal distribution, is a discrete probability distribution that models the number of failures in a sequence of independent and identically distributed Berno ...

, 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 if these events occur with a known const ...

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 probability theory and 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 ...

Student's t distribution In probability theory and statistics, Student's distribution (or simply the distribution) t_\nu is a continuous probability distribution that generalizes the standard normal distribution. Like the latter, it is symmetric around zero ...

chisquare distribution In probability theory and statistics, the \chi^2-distribution with k Degrees of freedom (statistics), degrees of freedom is the distribution of a sum of the squares of k Independence (probability theory), independent standard normal random vari ...

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 distribut ...

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 * Ex ...

and

gamma Gamma (; uppercase , lowercase ; ) 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 normally repr ...

distributions.

Examples

See also

References

Further reading