Search for probability and statistics terms on Statlect
Index > Glossary

Joint distribution function

by , PhD

The joint distribution function completely characterizes the probability distribution of a random vector X. When evaluated$\,$ at the point x, it gives the probability that each component of X takes on a value smaller than or equal to the respective component of x.

Table of Contents

Synonyms and acronyms

It is also called joint cumulative distribution function (abbreviated as joint cdf).


The following is a formal definition.

Definition The joint distribution function of a Kx1 random vector X is a function [eq1] such that:[eq2]where the components of X and x are denoted by $X_{k}$ and $x_{k}$ respectively, for $k=1,\ldots ,K$.


The joint distribution function can be used to the derive the marginal distributions of the single components of the random vector (see Random vectors). It is also used to check whether two ore more random variables are independent (see Independent random variables).

More details

More details about joint distribution functions can be found in the lecture entitled Random vectors.

Keep reading the glossary

Previous entry: Integrable random variable

Next entry: Joint probability density function

The book

Most of the learning materials found on this website are now available in a traditional textbook format.