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Lindley distribution

Probability distribution From Wikipedia, the free encyclopedia

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In probability theory and statistics, the Lindley distribution is a continuous probability distribution for nonnegative-valued random variables. The distribution is named after Dennis Lindley.[1]

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The Lindley distribution is used to describe the lifetime of processes and devices.[2] In engineering, it has been used to model system reliability.

The distribution can be viewed as a mixture of the Erlang distribution (with ) and an exponential distribution.

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Definition

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The probability density function of the Lindley distribution is:

where is the scale parameter of the distribution. The cumulative distribution function is:

for

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References

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