Power Quasi Lindley Power Series Class of Distributions: Theory and Applications - Soliman Hassan, Amal; Abd-Allah, Marwa (Thailand Statistician, 2023)
This article introduces a new class of lifetime distributions called the power quasi Lindley power series (PQLPS) which generalizes the Lindley power series class proposed by Warahena-Liyanage and Pararai (2015). This new class is obtained by compounding the power quasi Lindley and truncated power series distributions. The new class contains some new distributions such as power quasi Lindley geometric distribution, power quasi Lindley Poisson distribution, power quasi Lindley logarithmic distribution, power quasi Lindley binomial distribution and quasi-Lindley power series class of distributions. Some former works such as quasi Lindley geometric, Lindley geometric and Lindley Poisson distributions are special cases of the new compound class. Properties of the PQLPS class are studied, among them; quantile function, order statistics, moments and entropy. Some special models in the PQLPS class are provided. Maximum likelihood, least squares and weighted least squares methods are used to obtain parameter estimators of the PQLPS class. We assess and compare the performance of different parameter estimators of the power quasi Lindley Poisson model supported by a detailed simulation study. Additionally, the log-location-scale regression model based on a special member of the family is introduced. Two real data sets are employed to validate the distributions and the results demonstrate that the sub-models from the class can be considered as suitable models under several real situations.