The Pseudo-Lindley Alpha Power transformed distribution, mathematical characterizations and asymptotic properties

TL;DR

This paper introduces the Pseudo-Lindley alpha power transformed distribution (-APT), exploring its mathematical properties, estimation methods, asymptotic behavior, and demonstrating its flexibility and fit compared to existing distributions.

Contribution

It presents a novel generalization of the Pseudo-Lindley distribution using alpha power transformation, with detailed mathematical analysis and comparison to existing models.

Findings

-APT has tractable reliability and hazard rate properties.

Simulation shows -APT fits data as well as Lindley and Pseudo-Lindley distributions.

Extremal domain of attraction and extremal quantile functions are characterized.

Abstract

We introduce a new generalization of the Pseudo-Lindley distribution by applying alpha power transformation. The obtained distribution is referred as the Pseudo-Lindley alpha power transformed distribution (\textit{PL-APT}). Some tractable mathematical properties of the \textit{PL-APT} distribution as reliability, hazard rate, order statistics and entropies are provided. The maximum likelihood method is used to obtain the parameters' estimation of the \textit{PL-APT} distribution. The asymptotic properties of the proposed distribution are discussed. Also, a simulation study is performed to compare the modeling capability and flexibility of \textit{PL-APT} with Lindley and Pseudo-Lindley distributions. The \textit{PL-APT} provides a good fit as the Lindley and the Pseudo-Lindley distribution. The extremal domain of attraction of \textit{PL-APT} is found and its quantile and extremal quantile functions studied. Finally, the extremal value index is estimated by the double-indexed Hill's estimator (Ngom and Lo, 2016) and related asymptotic statistical tests are provided and characterized.