A 3-Component Mixture of Exponential Distribution Assuming Doubly Censored Data: Properties and Bayesian Estimation

DOI

10.2991/jsta.d.200508.002How to use a DOI?

Keywords

Mixture model; Doubly censoring sampling; Priors; Bayes estimators; Loss function; Posterior risks

Abstract

The output of an engineering process is the result of several inputs, which may be homogeneous or heterogeneous and to study them, we need a model which should be flexible enough to summarize efficiently the nature of such processes. As compared to simple models, mixture models of underlying lifetime distributions are intuitively more appropriate and appealing to model the heterogeneous nature of a process in survival analysis and reliability studies. Moreover, due to time and cost constraints, in the most lifetime testing experiments, censoring is an unavoidable feature. This article focuses on studying a mixture of exponential distributions, and we considered this particular distribution for three reasons. The first reason is its application in reliability modeling of electronic components and the second important reason is its skewed behavior. Similarly, the third and the most important reason is that exponential distribution has the memory-less property. In particular, we deal with the problem of estimating the parameters of a 3-component mixture of exponential distributions using type-II doubly censoring sampling scheme. The elegant closed-form expressions for the Bayes estimators and their posterior risks are derived under squared error loss function, precautionary loss function and DeGroot loss function assuming the noninformative (uniform and Jeffreys') and the informative priors. A detailed Monte Carlo simulation and real data studies are carried out to investigate the performance (in terms of posterior risks) of the Bayes estimators. From results, it is observed that the Bayes estimates assuming the informative prior perform better than the noninformative priors.

Copyright

© 2020 The Authors. Published by Atlantis Press SARL.

Open Access

This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - Muhammad Tahir
AU  - Muhammad Aslam
AU  - Muhammad Abid
AU  - Sajid Ali
AU  - Mohammad Ahsanullah
PY  - 2020
DA  - 2020/05/20
TI  - A 3-Component Mixture of Exponential Distribution Assuming Doubly Censored Data: Properties and Bayesian Estimation
JO  - Journal of Statistical Theory and Applications
SP  - 197
EP  - 211
VL  - 19
IS  - 2
SN  - 2214-1766
UR  - https://doi.org/10.2991/jsta.d.200508.002
DO  - 10.2991/jsta.d.200508.002
ID  - Tahir2020
ER  -