A Compounded Probability Model for Decreasing Hazard and its Inferential Properties

TL;DR

This paper introduces a new single-parameter distribution derived from exponential and Lindley distributions to model early failure problems, analyzing its properties and comparing its performance with existing decreasing hazard models.

Contribution

A novel compounded distribution based on exponential and Lindley distributions is proposed, with derived properties and an application to real data for early failure modeling.

Findings

Distribution has decreasing hazard rate

Distribution is positively skewed

Performs well compared to existing models on real data

Abstract

There are some real life issues that are exists in nature which has early failure. This type of problems can be modelled either by a complex distribution having more than one parameter or by finite mixture of some distribution. In this article a single parameter continuous distribution is introduced to model such type of problems. The base line distribution is exponential and it is compounded by lindley distribution. Some important properties of the proposed distribution such as distribution function, survival function, hazard function and cumulative hazard function are derived. The maximum likelihood estimate of the parameter is obtained which is not in closed form, thus iteration procedure is used to obtain the estimate of parameter. The moments of the proposed distribution does not exist thus median and mode is obtained. The distribution is positively skewed and the hazard rate of this distribution is decreasing. Some real data sets are used to see the performance of proposed distribution with comparison of some other competent distributions of decreasing hazard using Likelihood, AIC, AICc, BIC and KS statistics.