On the Alpha Power Transformed Power Lindley Distribution

Amal S Hassan,Rokaya E Mohamd,Sharifah Alrajhi,M Elgarhy

doi:10.1155/2019/8024769

Abstract

In this paper, we introduce a new generalization of the power Lindley distribution referred to as the alpha power transformed power Lindley (APTPL). The APTPL model provides a better fit than the power Lindley distribution. It includes the alpha power transformed Lindley, power Lindley, Lindley, and gamma as special submodels. Various properties of the APTPL distribution including moments, incomplete moments, quantiles, entropy, and stochastic ordering are obtained. Maximum likelihood, maximum products of spacings, and ordinary and weighted least squares methods of estimation are utilized to obtain the estimators of the population parameters. Extensive numerical simulation is performed to examine and compare the performance of different estimates. Two important data sets are employed to show how the proposed model works in practice.

Highlights

The one-parameter Lindley distribution was primarily proposed by Lindley [1] as an alternative model for data with a nonmonotone hazard rate shape
A random variable X is said to have a threeparameter alpha power transformed power Lindley (APTPL) distribution with the scale parameter θ >0 and shape parameters α, β >0, if its cdf is of the form
Various statistical properties are discussed such as moments, moment generating function, incomplete moments, and quantile function

Summary

Introduction

The one-parameter Lindley distribution was primarily proposed by Lindley [1] as an alternative model for data with a nonmonotone hazard rate shape. The Lindley distribution has only increasing failure rate which has been identified as a major difficulty in lifetime analysis To overcome this situation, many generalizations of the Lindley distribution have been introduced in literature. The alpha power transformation (APT) is one of the procedures that make the distributions richer and flexible to model the real life data. The APT has been proposed by Mahdavi and Kundu [13] with the parameter α to incorporate skewness to the base distribution. Mahdavi and Kundu [13] applied the APT method to the exponential distribution and they studied various properties of the alpha power exponential distribution. Following the similar idea of Mahdavi and Kundu [13], we introduce a new three-parameter distribution, the so-called APTPL distribution.

The APTPL Model

Statistical Properties

Estimation

Real Data Analysis

Findings

Concluding Remarks