Univariate distribution

In statistics, a univariate distribution is a probability distribution of only one random variable. This is in contrast to a multivariate distribution, the probability distribution of a random vector (consisting of multiple random variables).

Examples

Continuous uniform distribution

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

Binomial distribution with normal approximation for n = 6 and p = 0.5

Other examples of discrete univariate distributions include the binomial, geometric, negative binomial, and Poisson distributions.^[1] At least 750 univariate discrete distributions have been reported in the literature.^[2]

Examples of commonly applied continuous univariate distributions^[3] include the normal distribution, Student's t distribution, chisquare distribution, F distribution, exponential and gamma distributions.

See also

• Univariate
• Bivariate distribution
• List of probability distributions