Power Modified 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 modified
Lindley distribution. Its main feature is to operate a simple trade-off among the general ized exponential, Weibull and gamma distributions, offering an alternative to these three
well-established distributions. The proposed model turns out to be quite flexible: 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 different loss functions. In addi tion, bootstrap confidence intervals are provided to compare with Bayes credible intervals.
Besides, log power modified Lindley regression model for censored data is proposed. Two
real data sets are analyzed to illustrate the flexibility and importance of the proposed
model.