Estimation of lifetime parameters of the modified extended exponential distribution with application to a mechanical model

Abstract

The issue of this paper is the inference about the parameters of modified extended exponential distribution (MExED) planned on the progressively type-II censored (Prog -II- C) samples. The maximum likelihood and Bayesian estimates are procured for the parameters of MExED. Approximate confidence intervals (ACIs), the reliability and risk functions are estimated based on the asymptotic distribution of maximum likelihood estimates (MLEs) and delta method approach. Moreover, Bayesian estimates are obtained for symmetric and asymmetric loss functions such as squared error loss (SEL) and LINEX loss functions. Gibbs within Metropolis–Hasting samplers procedure is applied for using the Markov chain Monte Carlo (MCMC) technique to get on the Bayes estimates of the unknown parameters and their credible intervals (CRIs). Finally, a real-life data set, which represents the breakdown of some mechanical components, is considered an application of the proposed methods.

Keywords:

• Markov chain Monte Carlo
• Maximum likelihood estimators
• Modified extended exponential distribution
• Risk and reliability analysis

MATHEMATICS SUBJECT CLASSIFICATION (2010):

• 62N01
• 62N02
• 62N05