BAYESIAN ESTIMATION OF FOUR PARAMETERS ADDITIVE CHEN-WEIBULL DISTRIBUTION (FUDMA JOURNAL OF SCIENCES, 2022)
Models with bathtub-shaped failure rate function have been widely accepted in the field of reliability and medicine and are particularly useful in reliability related decision making and cost analysis. In this study, the additive Chen-Weibull (ACW) distribution with increasing and bathtub-shaped failure rates function is studied using Bayesian and non-Bayesian approach using two real data set. The Bayes estimator were obtained by assuming non-informative prior (Half-Cauchy) under square error loss function (SELF), the Laplace Approximation and Monte Carlo Markov Chain (MCMC) techniques conducted in R were used to approximate the posterior distribution of ACW model. In addition, the maximum product of spacing method (MPS) of estimation is also considered using mpsedist function in BMT package in R with good set of initial values of parameters. We compared the performance of the two difference estimation methods by using Kolmogorov-Smirnov test. And the result showed that MPSEs method outperformed Bayesian approach
Keywords: Bayes estimators, prior distribution, square error loss function, Chen Distribution, Weibull distribution