Joint distribution

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A general term referring to the distribution of several random variables defined on the same probability space. Let be random variables defined on a probability space and taking values in measurable spaces (cf. Measurable space) . The joint distribution of these variables is the function of sets , defined by

In connection with joint distributions, one speaks of the joint distribution function and of the joint probability density.

If are ordinary real random variables, then their joint distribution is the distribution of the random vector in -dimensional Euclidean space (see Multi-dimensional distribution). If , , is a stochastic process, then the joint distributions of the variables for are called the finite-dimensional distributions of the stochastic process .


[1] Yu.V. [Yu.V. Prokhorov] Prohorov, Yu.A. Rozanov, "Probability theory, basic concepts. Limit theorems, random processes" , Springer (1969) (Translated from Russian)



[a1] P. Billingsley, "Probability and measure" , Wiley (1979)
[a2] J.L. Doob, "Stochastic processes" , Wiley (1953)
How to Cite This Entry:
Joint distribution. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by A.V. Prokhorov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article