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."Fiducial distributions and Bayes’ theorem", Journal of the Royal Statistical Society B 1958 vol.20 p.102-107
The Lindley distribution is used to describe the lifetime of processes and devices."Lindley distribution and its application", Mathematics and computers in simulation 2008 vol.78(4) p.493-506 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.
Definition
The probability density function of the Lindley distribution is:
where is the scale parameter of the distribution. The cumulative distribution function is:
for
References