A new 3-parameter extension of generalized lindley distribution

TL;DR

This paper introduces a new three-parameter extension of the Lindley distribution, offering enhanced flexibility for modeling various failure rate behaviors, with applications demonstrated on real data and reliability analysis.

Contribution

The paper proposes a novel three-parameter Lindley distribution with diverse hazard functions, deriving properties, estimators, and demonstrating practical applications.

Findings

Flexible distribution with IFR, DFR, and upside-down hazard functions

Maximum likelihood estimators and confidence intervals derived

Successful modeling of real data and reliability analysis

Abstract

Here, we introduce a new class of Lindley generated distributions which results in more flexible model with increasing failure rate (IFR), decreasing failure rate(DFR) and up-side down hazard functions for different choices of parametric values. We explore, various distributional properties including limiting distribution of extreme order statistics explored. Maximum likelihood estimators and the confidence intervals of the parameters are obtained. The applicability of the proposed distribution is shown through modelling two sets of real data on bladder cancer patients and waiting time in a queue. Further, we carry out stress-strength analysis for applying the model in system reliability studies.