Statistics How To

Univariate Distribution

Share on

Probability Distributions >

A univariate distribution is the probability distribution of a single random variable. For example, the energy formula (x – 10)2/2 is a univariate distribution because only one variable (x) is given in the formula. In contrast, bivariate distributions have two variables and multivariate distributions have two or more.

Types of Univariate Distribution

Hundreds of univariate distributions exist: some are more common than others. Many of these probability distributions are closely connected via transformations, some of which can be inverted. Transformations can include:

The following image shows how some of the major univariate distributions are connected. Discrete distributions are in blue; Continuous distributions are in green. Common sampling distributions are in orange. For more information about these connections, read Interconnectivity of Univariate Probability Distributions on my Data Science Central blog.

univariate distribution

Univariate distributions are connected via transformations.




Leemis, L. & McQueston, J. Teacher’s Corner: Univariate Distribution Relationships. Retrieved February 19, 2021 from
Univariate Distribution. Retrieved February 19, 2021 from:

Stephanie Glen. "Univariate Distribution" From Elementary Statistics for the rest of us!

Need help with a homework or test question? With Chegg Study, you can get step-by-step solutions to your questions from an expert in the field. Your first 30 minutes with a Chegg tutor is free!

Comments? Need to post a correction? Please post a comment on our Facebook page.