Statistical Inference Of Two Weibull Populations Based On Joint Records

Based on the observed lower-joint record values,inter-record times and record indicators,this paper studies the statistical inference problem of two Weibull populations with the same shape parameters.First of all,the maximum likelihood estimation(MLEs)of the parameters in the model is derived.Secondly,we consider the Bayesian estimation under the square error loss(SEL)function.As we all know,the performance of Bayesian estimation is related to the choice of prior distribution.Generally,when the parameters in the model are unknown,the general method of Bayesian estimation is to specify a general joint prior for the parameters.However,when Bayesian estimation of the model is based on the general joint prior,we can not get the explicit form of the expectation of the marginal posterior distribution of each parameter,so we use the Markov chain Monte Carlo(MCMC)method and Gibbs algorithm to solve this problem.MCMC method is very effective,but this method leads to computational complexity.For solving this problem and simplifying Bayesian analysis,this paper also discusses another method,Soland's method.Soland method is to consider a series of joint priors distribution,that is,to specify the conjugate prior for the scale parameter and the discrete prior for the shape parameter.By using this prior distribution,we haved derived the explicit expression of Bayesian estimators of model parameters,which can simplify the calculation.In addition,the confidence interval estimation of parameters is also discussed.Finally,the MATLAB software is used to carry out numerical simulation,and the deviation and mean square error between MLEs and Bayesian estimation are calculated and compared.The results show that the two Bayesian estimation methods discussed in this paper are both ideal and better than the maximum likelihood estimation method.