On finite 3-component mixture of exponential distributions: Properties and estimation

Muhammad Tahir,Zawar Hussain,Akbar Ali Khan,Muhammad Aslam

doi:10.1080/23311835.2016.1275414

Abstract

AbstractTo study reliability problems, life time and survival analysis, a new mixture model, called the 3-component mixture of the Exponential distributions, is introduced. This study is mainly concerned with the problem of investigating the different statistical properties of the newly developed 3-component mixture of Exponential distributions. Firstly, some basic properties of the 3-component mixture model are discussed. Secondly, we discuss hazard rate function, cumulative hazard rate function, reversed hazard rate function, mean residual life function, and mean waiting time function. Different measures of entropy and inequality indices are also discussed. Closed form expressions of the density functions of order statistics and their statistical properties are derived. Finally, the parameters of the proposed mixture distribution are estimated by making use of the maximum likelihood approach under complete and censored sampling. The results on maximum likelihood estimation are also supported through a s...

Highlights

During the last few decades, finite mixtures of life distributions have been proved of considerable interest both in terms of their methodological development and practical applications
The mixture of probability density functions from the same family is known as type-I mixture model
We study the reliability properties of the 3-component mixture of Exponential distributions (3-CMED)

Summary

PUBLIC INTEREST STATEMENT

In the field of industrial engineering, an engineering system may fail due to different causes. These causes of failures may be suitably modeled by the mixture distributions. We considered a situation where component failures follow a 3-CMED. The results in this study are helpful in identifying the causes of failure of an engineering systems and estimating its future life, chances of hazards in future, and behavior of its decay. A common man, not an expert in reliability modeling, can use the results of this study for making decision about lifetimes of a system where causes of the failure follow a 3-CMED

Introduction

ML estimates t