Some new and generalized distributions for reliability and lifetime data analysis

Abstract

New distributions namely, Lindley-Weibull Power Series (LWPS) class of distributions and the special case called Lindley-Weibull logarithmic (LWL) distribution, a new gamma generalized Lindley log-logistic (GELLLoG) distribution, Marshall-Olkin Lindley log-logistic (MOLLLoG) distribution and half logistic log-logistic Weibull (HLLLoGW) distribution and their sub-models are presented. Structural properties including hazard and reverse hazard functions, quantile function, moments, conditional moments, mean deviations, Bonferroni and Lorenz curves, Renyi entropy, distribution of order statistics ´ and maximum likelihood estimates of the above proposed distributions are presented. Applications of the presented models to real data sets are given in order to illustrate the applicability and usefulness of the proposed distributions. These distributions were also compared to some non-nested models.