A new lifetime model with decreasing failure rate

TL;DR

This paper introduces a new lifetime distribution combining exponential and Poisson-Lindley models, providing properties, estimation methods, and applications to real data for improved survival and reliability analysis.

Contribution

The paper presents a novel lifetime distribution with derived properties and estimation techniques, expanding tools for survival and reliability studies.

Findings

Derived density, failure rate, and moments of the new distribution

Maximum likelihood estimation methods discussed for large samples

Application to real data sets demonstrating model usefulness

Abstract

In this paper we introduce a new lifetime distribution by compounding exponential and Poisson-Lindley distributions, named exponential Poisson-Lindley distribution. Several properties are derived, such as density, failure rate, mean lifetime, moments, order statistics and R\'enyi entropy. Furthermore, estimation by maximum likelihood and inference for large sample are discussed. The paper is motivated by two applications to real data sets and we hope that this model be able to attract wider applicability in survival and reliability.