The Estimation And Goodness Of Fit Tests For The Scale Family Based On Complex Censored Samples

In this article,we mainly study the parameter estimation and the goodness of fit test problems of inverse Rayleigh distributions and scale family under the complete data and complex censoring scheme data.Three parts are included in this design:parameter estimation,the goodness of fit test and numerical experiments.The estimation problem of the inverse Rayleigh distribution under the progres-sively Type-II censored samples and the general progressively Type-II censored samples are studied,meanwhile the maximum likelihood estimates and approximate maximum likelihood estimates are obtained.And the estimates based on the pivotal method are also obtained,based on which the asymptotic confidence interval is derived.In addi-tion,the method is extended to the distribution of arbitrary scale families,and the point estimates of the scale families based on the pivotal quantity method under the general progressively Type-II censored samples are obtained;The goodness of fit test of the inverse Rayleigh distribution under the progressively Type-II censored samples is investigated.Based on the estimation,the goodness of fit test based on the entropy method and the non-entropy method is studied,and the power analysis is performed.At the same time,the method is also extended to scale family,and two goodness of fit test statistics for the scale family are obtained.We illustrate our method on the scaled half-logistic distribution and power analysis is performed.Finally,we use Monte Carlo simulation and real data analysis to compare the es-timated results of different methods,mainly using bias,mean square error,power,and average interval coverage as reference indicators in each section.