A quasi Lindley distribution

TLDR: In this article, a two-parameter Quasi Lindley distribution (QLD) has been introduced and its moments, failure rate function, mean residual life function and stochastic orderings have been discussed.

Abstract: A two-parameter Quasi Lindley distribution (QLD), of which the Lindley distribution (LD) is a particular case, has been introduced. Its moments, failure rate function, mean residual life function and stochastic orderings have been discussed. It is found that the expressions for failure rate function, mean residual life function, and stochastic orderings of the QLD shows its flexibility over Lindley distribution and exponential distribution. Although, the QLD has two parameters, the expressions for coefficients of variation, skewness, and kurtosis depend upon only one parameter. The maximum likelihood method and the method of moments have been discussed for estimating its parameters. The distribution has been fitted to some data-sets to test its goodness of fit to which earlier the Lindley distribution has been fitted by others and it is found that to almost all these data-sets the QLD provides closer fits than those by the Lindley distribution.   Key words: Lindley distribution, moments, failure rate function, mean residual life function, stochastic ordering, estimation of parameters, goodness of fit. .