In applied statistics, the Marshall–Olkin exponential distribution is any member of a certain family of continuous multivariate probability distributions with positive-valued components.

It was introduced by Albert W. Marshall and Ingram Olkin.

[1] One of its main uses is in reliability theory, where the Marshall–Olkin copula models the dependence between random variables subjected to external shocks.

be a set of independent, exponentially distributed random variables, where

is called the Marshall–Olkin exponential distribution with parameters

Then there are seven nonempty subsets of { 1, ..., b } = { 1, 2, 3 }; hence seven different exponential random variables: Then we have: