Statistical Inference Studies For Gompertz Distribution Under Complex Censored Schemes

This paper mainly studies the parameter statistical inference of Gompertz lifetime distribution under complex censoring scheme data.The distribution of Gompertz plays an important role in real production and life.In this paper,point estimations,interval estimations,numerical experiments and real data analysis are mainly studied.This paper mainly considers two different data models,namely,adaptive type-II hybrid censoring scheme model and progressive type-II hybrid competing risks censoring model.In recent years,these two models have been widely discussed and studied by researchers.Therefore,the research work of this paper is of certain prospective and strong application value.This paper firstly discusses the statistical inference of Gompertz distribution under adaptive type-II hybrid censoring data.From the frequentist,the maximum likelihood estimation of unknown parameters and the corresponding asymptotic confidence interval are given in this paper.The point estimation under stochastic EM algorithm and the interval estimation under Bootstrap method are also given.From the view of Bayes statistics,based on the Gamma prior,the estimation algorithm of unknown parameters under the loss of squared error and linear index is given.Secondly,this paper discusses the statistical inference of Gompertz distribution under the progressively type-II hybrid competing risks data.From the point of frequentist,the maximum likelihood method is used to obtain the point estimation of unknown parameters,and the existence and uniqueness of the estimation are first proved from the theory.Further,using the asymptotic normality of the maximum likelihood estimation,this paper obtains a progressive confidence interval.The Bootstrap confidence interval is also given in this paper,which includes the Bootstrap-p and Bootstrap-t methods.For comparison,this paper studies the point estimation and interval estimation under Bayesian.Finally,the given inference algorithm is numerically simulated.The two different data generation algorithms studied are given.Perform and evaluate multigroup contrast simulation experiments on the generated data,including,contrast between different censoring schemes,different parameter quantities,different stop time T,different bias constants,etc.The simulation results show that the proposed algorithms have excellent estimation effect under most experimental parameters and have great practical values.Therefore,in this paper,the proposed algorithm is applied to two sets of practical data,using Gompertz distribution fitting data to estimate the unknown parameters.