Reliability Estimation For The Different Life Distributions Based On The Various Censored Sample

In this paper,we consider estimating the parameters,reliability function and fail-ure rate function of the different life distributions based on the various censored sample or complete sample.Point estimation,interval estimation and numerical experiment are obtained in this article.Three parts are included in this design:Inverse weibull esti-mation under the condition of complete data,we obtain the maximum likelihood esti-mator(MLE)of reliability function RA and its asymptotic distribution.Note that MLEs don't have explicit forms,we present the approximate maximum likelihood estima-tor(AMLE)of/RA.The confidence interval of RA can be obtained using the asymptotic distribution.The two bootstrap confidence intervals are proposed.By using Gibbs sam-pling technique,we obtain the Bayesian estimator of RA and the corresponding credible interval for RA is given;bathtub-shaped estimation under the condition of the progres-sive first-failure censored sample,the MLEs and Bayes estimators under squared error loss function are derived.We obtain the asymptotic confidence intervals for the parame-ters using the observed Fisher information matrix.The parametric bootstrap confidence intervals of reliability characteristics are also proposed.Lindley approximation pro-cedure is adopted to establish Bayes estimates;inverse exponential estimation under the condition of the progressively Type-II censored sample,we address a approach by approximating the likelihood function to get the explicit estimator firstly in this pa-per.Next,we propose a simple estimation method for the parameter based on the pivotal quantity.We show that this proposed approach gives a simpler estimation equation than the MLE equation.Especially to deserve to be mentioned,we examine through simula-tions and discover that this estimator is more effective than the MLE in terms of bias,particularly when the observed sample size is small.Furthermore,we derive the con-fidence interval of scale parameter from pivotal quantity and find that coverage prob-abilities are matched to the nominal levels in all cases.Finally,the different proposed methods are compared through Monte Carlo simulations and a real data is presented for illustrative proposes.