Goodness-of-fit Test And Statistical Inference Of Rayleigh And Generalized Rayleigh Distributions Based On Complex Data Models

This paper studies the statistical inference and goodness-of-fit test of general-ized Rayleigh distribution and Rayleigh distribution with complex censored data.In the aspect of statistical inference,we mainly focus on two censoring models,i.e.Type-II progressive censoring with binomial removals and progressively Type-II cen-sored competing risks model.Based on the sample data following the generalized Rayleigh distribution,we conduct statistical inference for the unknown parameters and reliability characteristics.The main methods we use are Bayesian estimation method and classical frequency methods such as maximum likelihood.For the Type-II progressive censoring with binomial removals model,through extensive Monte Carlo simulation experiments,we have studied different hyperparameters as well as symmetric and asymmetric loss functions in the Bayesian estimation procedure.A real industrial case is presented to justify and illustrate the proposed methods.We also investigate the expected experimentation time and discuss the influence of the parameters on the termination point.For the progressively Type-II censored competing risks model,the cases when the parameters of the latent lifetime distri-butions are different or common are both discussed,and the procedure of hypothesis test by using likelihood ratio test statistics is given in the real-data analysis sec-tion.Maximum likelihood estimates are obtained,where the existence of the point estimators is proved,and the confidence intervals are established via the observed Fisher information matrix as well.Bayesian estimates of unknown parameters and reliability characteristics are derived under symmetric and asymmetric loss func-tions,and Monte Carlo Markov Chain sampling method is used to compute the Bayesian point estimates and the highest posterior density credible intervals.In addition,Bootstrap methods are also considered to obtain bias-corrected point esti-mates and approximate confidence intervals.Finally,the optimal censoring scheme issue is studied.In the aspect of the goodness-of-fit test,we propose four statistics to conduct tests for Rayleigh distribution based on progressively Type-II censored data,where a cumulative entropy and its upper and lower bounds as well as the sample spacings are used respectively,and the corresponding statistics are denoted by T_E,T_U,T_Land T_S.Especially,the null distribution of T_Stest statistic is derived.The respective performance of these statistics is explored against different alternatives,and the power comparisons with some existing goodness-of-fit test statistics are studied via a wide range of Monte Carlo simulations.The results reveal that T_Sis more effective than the others in most cases;all test statistics have a remarkable performance for the alternative hypothesis with decreasing hazard function.Finally,the proposed statistics are applied in an illustrative example.There are 15 figures,34 tables and 52 references.