Univariate distribution
Instatistics,aunivariate distributionis aprobability distributionof only onerandom variable.This is in contrast to amultivariate distribution,theprobability distributionof arandom vector(consisting of multiple random variables).
Examples[edit]
One of the simplest examples of adiscrete univariate distributionis thediscrete 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 univariatecontinuous uniform distributionon 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 thebinomial,geometric,negative binomial,andPoisson distributions.[1]At least 750 univariate discrete distributions have been reported in the literature.[2]
Examples of commonly appliedcontinuous univariate distributions[3]include thenormal distribution,Student's t distribution,chisquare distribution,F distribution,exponentialandgammadistributions.
See also[edit]
References[edit]
- ^Johnson, N.L., Kemp, A.W., and Kotz, S. (2005) Discrete Univariate Distributions, 3rd Edition, Wiley,ISBN978-0-471-27246-5.
- ^Wimmer G, Altmann G (1999) Thesaurus of univariate discrete probability distributions. STAMM Verlag GmbH Essen, 1st ed XXVIIISBN3-87773-025-6
- ^Johnson N.L., Kotz S, Balakrishnan N. (1994) Continuous Univariate Distributions Vol 1. Wiley Series in Probability and Statistics.
Further reading[edit]
- Leemis, L. M.; McQueston, J. T. (2008)."Univariate Distribution Relationships"(PDF).The American Statistician.62:45–53.doi:10.1198/000313008X270448.
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