Power Modi ed Lindley Distribution: Properties, Classical and Bayesian Estimation and Regression Model with Applications

Abstract

In this article, we explore a new probability density function, called the power modi ed Lindley distribution. Its main feature is to operate a simple trade-o among the general ized exponential, Weibull and gamma distributions, o ering an alternative to these three well-established distributions. The proposed model turns out to be quite exible: its probability density function can be right skewed and its associated hazard rate function may be increasing, decreasing, unimodal and constant. First the model parameters of the proposed distribution are obtained by the maximum likelihood method. Next, Bayes estimators of the unknown parameters are obtained under di erent loss functions. In addi tion, bootstrap condence intervals are provided to compare with Bayes credible intervals. Besides, log power modi ed Lindley regression model for censored data is proposed. Two real data sets are analyzed to illustrate the exibility and importance of the proposed model.