Univariate Distribution

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.

Discrete:

Continuous:

References

Leemis, L. & McQueston, J. Teacher’s Corner: Univariate Distribution Relationships. Retrieved February 19, 2021 from Academia.edu https://www.academia.edu/6823496/Univariate_Distribution_Relationships.
Univariate Distribution. Retrieved February 19, 2021 from: http://www.math.wm.edu/~leemis/chart/UDR/about.html