Power Modi ed Lindley Distribution: Properties, Classical and Bayesian Estimation and Regression Model with Applications
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Date
2023-07
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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.