A new four-parameter lifetime distribution

Abstract

Generalizing lifetime distributions is always precious for applied statisticians. In this paper, we introduce a new four-parameter generalization of the exponentiated power Lindley (EPL) distribution, called the exponentiated power Lindley geometric (EPLG) distribution, obtained by compounding EPL and geometric distributions. The new distribution arises in a latent complementary risks scenario, in which the lifetime associated with a particular risk is not observable; rather, we observe only the maximum lifetime value among all risks. The distribution exhibits decreasing, increasing, unimodal and bathtub-shaped hazard rate functions, depending on its parameters. It contains several lifetime distributions as particular cases: exponentiated power Lindley (EPL), new generalized Lindley (NGL), generalized Lindley (GL), power Lindley (PL) and Lindley geometric (LG) distributions. We derive several properties of the new distribution such as closed-form expressions for the density, cumulative distribution function, survival function, hazard rate function, the rth raw moment, and also the moments of order statistics. Moreover, we discuss maximum likelihood estimation and provide formulas for the elements of the Fisher information matrix. Simulation studies are also provided. Finally, two real data applications are given for showing the flexibility and potentiality of the new distribution.

A General Transmuted Family of Distributions

“…We now present the genesis of cubic transmuted family of distributions given in (3) in context with distribution of order statistics and with T − X family of distributions in following two theorems.…”

New General Transmuted Family of Distributions with Applications

“…This transmuted family of distributions introduced by Shaw and Buckley (2007), has opened doors to modify the available probability distributions to capture the quadratic behavior of the data. The quadratic transmuted family was further highlighted and extended by Tsokos (2009, 2011); Yousof et al (2015); Alizadeh et al (2016); Merovci et al (2016) and Nofal et al (2017). The quadratic transmuted distributions are very common in the literature.…”