The Inferences And Goodness-of-fit Tests For Some Life Distributions Based On The Censored Samples

Based on different censored samples,this paper studies some statistical inferences of parameters and goodness-of-fit tests for some typical life distributions.As for the inferences of parameters,it mainly includes the point estimation and interval estimation methods.In the study of goodness-of-fit tests for distributions,this paper obtains new statistics to test the distribution fitting under censoring schemes.This paper mainly discusses three aspects:Firstly,the parameters of two-parameter Rayleigh distribution are estimated under the progressive first failure censored samples.We use pivotal quantities to estimate the parameters in order to solve the computational difficulty of the maximum likelihood estimation.By using the pivotal method,the point and interval estimators for two-parameter Rayleigh distribution are derived.Secondly,this paper investigates the inference of the lifetime performance index for Gompertz distribution based on the progressive first failure censoring.By using pivotal quantities,the hypothesis tests are established to determine whether the lifetime performance index CL is qualified.The point estimation and interval estimation of CL are obtained,and the test processes of the lifetime performance index for Gompertz distribution are set up.In the third part,aiming at two common life distributions,two-parameter exponen-tial distribution and normal distribution,this paper studies the goodness-of-fit test with left censored samples.By improving Kullback-Leibler information,the test statistics for the goodness-of-fit test towards two-parameter exponential distribution and normal distribution under the left censoring are constructed.In this paper,Monte Carlo simulations and real data examples are carried out for the above three aspects.The results show that the inference methods and goodness-of-fit tests proposed in this paper are effective and feasible,which illustrates the application value of the research.