Statistical Inference Of Three Different Lifetime Distributions Based On High-dimensional Complex Censored Data

This paper mainly discusses the statistical inference of three different lifetime distribution under high-dimensional complex censored data,including parameter estimation,interval estimation,testing procedure algorithm and numerical experiments.The article consists of the following three parts:Exponentiated half logistic distribution(EHLD): we discuss the parameter and interval estimation of the scale parameter in a EHLD under progressive type II and general progressive type II censoring.We first obtain the maximum likelihood of the scale parameter.Then,we use Taylor expansion and establishment of pivotal quantity to obtain three approximate maximum likelihood estimates.We also obtain the asymptotic confidence interval of the scale parameter based on the established pivotal quantity.Generalized Pareto distribution(GPD): based on progressive type II censored data,we obtain maximum likelihood estimates and Bayesian estimates of two unknown parameters,reliability and hazard functions of GPD,and by using the Delta method and the Bootstrap algorithm derive their corresponding approximate confidence intervals.Lomax distribution: based on progressive type I interval censored data,we obtain the maximum likelihood estimate and approximate confidence interval for the lifetime performance index of products that obey the Lomax distribution.For the two cases of unknown parameters and given scale parameter,we propose two testing procedure algorithms for lifetime performance index to determine if the products' lifetime performance reaches the required level.Finally,we perform simulation research on the methods proposed above and analyze three sets of actual data sets obeying different lifetime distributions in order to verify the effectiveness of the previously proposed methods.