Estimations for Pareto Model Using General Progressive Censored Data and Asymmetric Loss

Abstract

In this article, based on a general progressively Type-II censored data from the Pareto distribution of the second kind, we consider Bayesian and classical estimations of the parameters as well as some survival time parameters, the reliability, and hazard functions. Recently, Howlader and Hossain (2002) obtained Bayesian survival estimation using some approximation forms based on: quadratic loss function, non informative prior, and usually Type-II censored data. In this article, we propose to carry out a Bayesian estimation procedures based on: (i) informative prior for the shape parameter and discrete prior for the scale parameter of the model; (ii) both the symmetric loss function (squared error loss) and asymmetric loss function (linear-exponential (LINEX)) loss function; (iii) general progressively Type-II censored samples which include as a special cases: the regular doubly Type-II censored, progressively Type-II censored, usual Type-II right censored, and uncensored (complete) samples. The resulting Bayes estimates are obtained in closed form. Approximate confidence intervals for the parameters are constructed. Maximum likelihood estimators and their asymptotic variances are derived. One real data set has been analyzed for illustrative purposes. Finally, simulation study concerning different sample sizes and progressive censoring schemes were reported.