Bayesian reconstruction of the missing failure times in exponential distribution

In this paper, we consider the situations in which a middle part of the sample is lost or removed from the experiment. The left-censored sample and Type-II right-censored sample are special cases of this scheme. Point and interval reconstructors for lost failure times are obtained, while the underlying distribution is exponential. To illustrate the performance of the proposed procedures, two numerical examples based on the real data sets are presented. In the case of two-parameter, a simulation study has been done and also the sensitivity of the results to deviations from the true distribution is investigated.     

Reconstruction of the past lower record values in a proportional reversed hazard rate model

In this paper, the situation in which some lower records from a proportional reversed hazard rate model (PRHRM) are lost at the beginning of the experiment is considered. The reconstruction problem of the past lower records based on observed records from a PRHRM is discussed. Several various methods are used to obtain point reconstructors. More details are given for the Fréchet distribution. Three reconstruction intervals are also obtained and compared in the sense of the expected width for the case of Fréchet distribution. A data set representing the annual flood loss is applied to illustrate the proposed procedure in this paper. Eventually, some concluding remarks are presented.     

Estimation and prediction in the presence of an outlier under Type-II censoring

A single-outlier data set containing some independent random variables is considered such that all of observations expect one have the same distribution. To describe the model of interested, a location-scale family of distributions is used and the estimation problem of the parameters is studied when the data are collected under Type-II censoring scheme. Moreover, three different predictors are presented to predict the censored order statistics. They are also compared regarding both of mean squared prediction error and Pitman's measure of closeness criteria. The role of outlier parameter as well as censorship rate is studied on performance of proposed estimator and predictors. The results of the paper are illustrated via a real data set. Finally, some conclusions are stated.