Bayesian Analysis Of The Marshall-Olkin Bivariate Weibull Distribution

Marshall-Olkin bivariate Weibull distribution is an important content of reliability analysis and life test in statistics.This paper mainly discusses some methods of the Marshall-Olkin bivariate Weibull distribution parameter estimation.Firstly,this paper analyzes the characteristics of Marshall-Olkin bivariate Weibull distribution function.Because it is a mixture of an absolute continuous function and a singular function,and the different situations of the function image difference is great,it is known that Marshall-Olkin bivariate Weibull distribution is a complex distribution.Then,this paper proposes to use the importance sampling method to compute the Bayesian estimation of the Marshall – Olkin bivariate Weibull distribution.The method of importance sampling was proposed by Kundu and Gupta.Because the efficiency of the importance sampling method depends on the choice of the proposed distribution,we find that the performance of the importance sampling method becomes worse as the sample size gets larger.In order to avoid this problem,improve the accuracy of parameter estimation,this paper introduces latent variables to simplify the likelihood function,and uses MCMC algorithm of Gibbs sampling algorithm to estimate the unknown parameters.In order to further evaluate the effectiveness of the proposed method,we compare simulation results of the Bayesian method based on Gibbs sampling algorithm with maximum likelihood estimates using EM algorithm.We find that the parameter estimation of Bayesian method based on Gibbs sampling algorithm is better,even under the condition of the small sample size.Finally,analyse a real data examples to verify the conclusion.