On the Alpha Power Transformed Power Lindley Distribution

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.

Marshall Olkin Alpha Power Extended Weibull Distribution: Different Methods of Estimation based on Type I and Type II Censoring

“…For example, [8] introduced alpha power Weibull (APW) distribution, [9] introduced new AP transformed family of distributions, [10,11] introduced AP transformed Lindley and inverse Lindley respectively, [12] introduced AP transformed power Lindley distribution and [13] introduced AP inverse Weibull distribution, have done a lot of works on distributions based on AP transformation.…”

Marshall–Olkin Alpha Power Weibull Distribution: Different Methods of Estimation Based on Type-I and Type-II Censoring

“…Considerable work in distributions based on AP transformation had been done; for example, see the works of Nassar et al [9], Elbatal et al [10], Dey et al [11,12], Hassan et al [13,14], Basheer [15], and Almetwally and Ahmad [16].…”

Alpha Power Transformed Inverse Lomax Distribution with Different Methods of Estimation and Applications

“…In the literature, many probability distributions are generalized using this approach; for example, alpha power transformed Weibull (APTW) distribution in [9], APT generalized exponential distribution in [10], APT Lindley distribution in [11], APT extended exponential distribution in [12], alpha power inverted exponential distribution in [13], alpha power Inverse-Weibull distribution in [14], APT inverse-Lindley distribution in [15], APT power Lindley studied in [16], and APT Pareto distribution proposed in [17]. e main goal of this research article is to introduce a simpler and more flexible model called APT inverse Lomax (APTIL) distribution.…”