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Marshall–Olkin exponential distribution

Probability distribution in applied statistics From Wikipedia, the free encyclopedia

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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. [2] [3] [4]

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Definition

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Let be a set of independent, exponentially distributed random variables, where has mean . Let

The joint distribution of is called the Marshall–Olkin exponential distribution with parameters

Concrete example

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

Then we have:

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References

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