Parameter Estimation Under Two Kinds Of Type-? Censored

Type-? censored widely exist in aerospace,electronic engineering and other fields.And it has been valued by many experts in practice.The parameter estimation under type-? censored can provide reliable basis for researchers to analyze the overall characteristics and improve the quality of related products.For estimation problem of scale parameter and shape parameter of Weibull distribution based on type-? sequential hybrid censored,we use the maximum likelihood method to estimate the scale parameter and shape parameter of Weibull distribution,and obtain the maximum likelihood estimation of parameter.Then we prove that these maximum likelihood estimations have consistency and asymptotic normality.Finally,numerical simulation shows that the deviation,mean square error and confidence interval length of parameter estimator decrease with the increase of sample size.For nonparametric estimation problem of mean based on type-? censored,we use the cumulative risk function to construct the estimation equation of mean.And we use the empirical likelihood method to estimate mean and get the corresponding estimator.Then we prove that the log empirical likelihood ratio function of mean converges to the chi square distribution according to probability,and construct the confidence interval of mean.Finally,numerical simulation shows that the nonparametric estimator of mean has good stability and effectiveness.