The Power Inverse Lindley Distribution

TL;DR

This paper introduces the power inverse Lindley distribution, a new flexible model for survival data, derived from existing generalizations, with properties analysis, estimation behavior, and real data application demonstrating its effectiveness.

Contribution

It proposes the power inverse Lindley distribution, combining previous generalizations, and explores its properties, estimation, and practical application to survival data.

Findings

The distribution fits real survival data well.

Maximum likelihood estimators are studied.

Compared favorably with existing models.

Abstract

Several probability distributions have been proposed in the literature, especially with the aim of obtaining models that are more flexible relative to the behaviors of the density and hazard rate functions. Recently, a new generalization of the Lindley distribution was proposed by Ghitany et al. (2013), called power Lindley distribution. Another generaliza- tion was proposed by Sharma et al. (2015), known as inverse Lindley distribution. In this paper, a new distribution is proposed, which is obtained from these two generalizations and named power inverse Lindley distribution. Some properties of this new distribution and study of the behavior of maximum likelihood estimators are presented and discussed. It is also applied considering real data and compared with the fits obtained for already- known distributions. When applied, the power inverse Lindley distribution was found to be a good alternative for modeling survival data.