Binominal Mixture Lindley Distribution: Properties and Applications

Abstract

In this paper, we introduce a generalized mixture distribution, so-called the binomial mixture Lindley distribution (BMLD). The density function of this distribution is obtained by mixing binomial probabilities with gamma distribution. BMLD have various distributions as its special cases and posses various shapes for its hazard rate function including increasing, decreasing, bathtub shape and upside down bathtub shape depending on its parameters. Several mathematical, structural and statistical properties of the new distribution is presented such as moments, moment generating function, hazard rate function, vitality function, mean residual life function, inequality measures, entropy and extropy etc. The parameters of the model are estimated using the method of maximum likelihood and finally real life data sets are considered to illustrate the relevance of the new model by comparing it with some other lifetime models.