Lindley distribution and its generalization in poisson mixtures

Abstract

There are many distributions for modeling lifetime data, among the known parametric models, the most popular is Gamma, Beta, Poisson and Lindley. Lindley distribution is a way to describe the lifetime of a process. The exponential distribution is a close form of the Lindley distribution.Due to the popularity of the exponential distribution in statistics and many applied areas, the Lindley distribution has been overlooked in the literature. In this project we aim to construct the Lindley distribution using various number of parameters, then examine its properties namely moments,failure rate function and mean residual life function. The Poisson-Lindley mixture is examined in depth,both construction,properties and estimation of the distribution. Estimation of properties is determined using the method of moments, maximum likelihood method and the expectation maximization algorithm method .The methods are applied on various data sets and the results compared.