JOURNAL OF THE IRANIAN STATISTICAL SOCIETY (JIRSS)
Year:2007 | Volume:6 | Issue:2|Papers Count:6

The progressive censoring scheme is a method of data collecting in reliability and life testing which has been of intensified interest in recent years. In the present paper, we prove some characterization results on generalized Pareto distribution based upon the independency and expected values of some functions of progressive type-II right censored order statistics. 

In this paper we prove some stochastic comparisons results for progressive type II censored order statistics. The problem of stochastically comparing concomitants of the two progressive type II censored order statistics with possibly different schemes, under different kinds of dependence between X and Y is considered and it is proved that if Y is stochastically increasing (decreasing) in X, in some senses, then the concomitant variables Y R[i:n]’s are stochastically increasing (decreasing) according to usual stochastic ordering, hazard rate ordering, likelihood ratio ordering, mean residual life ordering and dispersive ordering.

This paper reviews some recent results on stochastic orders and dependence among order statistics when the observations are independent and follow the proportional hazard rates model.

For the samples coming from populations with identical distributions and finite variance, we evaluate the extreme deviations of expectations of spacings, when the assumption of independence is violated. The evaluations are described in the population standard deviation units. Attainability conditions and numerical results are presented.

The purpose of this paper is to investigate conditions on the underlying distribution functions and the parameters, on which the generalized order statistics are based on, to establish the usual stochastic and the likelihood ratio orderings of general p-spacings by conditioning on the right tail of another lower indexed generalized order statistics. Some potential applications are also given.

Sharp bounds for medians of L-statistics in the nonparametric statistical model with all continuous and strictly increasing distribution functions are given. As a corollary we conclude that L-statistics are very poor nonparametric quantile estimators.