Lindley distribution
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.
The Lindley distribution is used to describe the lifetime of processes and devices. In engineering, it has been used to model system reliability.
The distribution can be viewed as a mixture of the Erlang distribution 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