Conditional Ordering of Generalized Order Statistics Revisited (original) (raw)

ORDERING CONDITIONAL DISTRIBUTIONS OF GENERALIZED ORDER STATISTICS

Probability in The Engineering and Informational Sciences, 2007

The concept of generalized order statistics was introduced as a unified approach to a variety of models of ordered random variables. The purpose of this article is to establish the usual stochastic and the likelihood ratio orderings of conditional distributions of generalized order statistics from one sample or two samples, strengthening and generalizing the main results in Khaledi and Shaked [15], and Li and Zhao . Some applications of the main results are also given.

Some new results on likelihood ratio ordering and aging properties of generalized order statistics

Communications in Statistics - Theory and Methods, 2020

In this article, we first study the likelihood ratio ordering of generalized order statistics (GOS) in both one-sample and two-sample problems. Then, we establish the transmission of the increasing hazard rate and decreasing reversed hazard rate aging properties of GOS. To do this, we extend Karlin's basic composition theorem for the functions of three variables. Then, we settle certain open problems in this regard by providing some counterexamples. We further investigate similar transmission cases which have not been addressed in the literature so far.

On Multivariate Likelihood Ratio Ordering among Generalized Order Statistics and their Spacings

The most of the results obtained about stochastic properties of generalized order statistics and their spacings in the literature are based on equal model parameters. In this paper, with less restrictive conditions on the model parameters, we prove some new multivariate likelihood ratio ordering results between two sub-vectors of GOS's as well as two sub-vectors of p-spacings based on two continuous distribution functions. In particular, we apply the new results to obtain some computable bounds on the mean residual life of some unobserved progressive type II censored order statistics.

Characterizations via regression of generalized order statistics

Statistical Methodology, 2013

In this paper, we present some characterizations of distributions based on the regression of generalized order statistics. In the case of adjacent generalized order statistics, the conditional expectation of one generalized order statistic given the other one completely characterizes distributions depending on the type of regression function. In the case of non-adjacent generalized order statistics, the characterization of distributions using conditional expectations becomes more complicated. The results presented in the paper unify and extend some of the existing results involving order statistics and record values.

On Stochastic Comparisons of Concomitants of Generalized Order Statistics

JSAP , 2023

In this article, the problem of comparing concomitants of generalized order statistics (GOSs) in terms of different types of stochastic orders is considered. Some stochastic ordering results for compound random variables in the one-sample problems are recalled and extended. Analogous results are obtained in the two-sample setup. The derived results are used to compare concomitants of GOSs in both one-sample problems and two-sample problems. We also introduce some new joint stochastic orders (namely, the joint reversed hazard order and the joint convex order) and compare concomitants in terms of these orders.

Dependence orderings for generalized order statistics

Statistics & Probability Letters, 2005

Generalized order statistics (gOSs) unify the study of order statistics, record values, k-records, Pfeifer's records and several other cases of ordered random variables. In this paper we consider the problem of comparing the degree of dependence between a pair of gOSs thus extending the recent work of Ave´rous et al. [2005. J. Multivariate Anal. 94, 159-171]. It is noticed that as in the case of ordinary order statistics, copula of gOSs is independent of the parent distribution. For this comparison we consider the notion of more regression dependence or more stochastic increasing. It follows that under some conditions, for ioj, the dependence of the jth generalized order statistic on the ith generalized order statistic decreases as i and j draw apart. We also obtain a closed-form expression for Kendall's coefficient of concordance between a pair of record values. r

Multivariate Dispersive Ordering of Generalized Order Statistics

The concept of generalized order statistics (GOSs) was introduced as a unified approach to a variety of models of ordered random variables. The purpose of this paper is to investigate conditions on the underlying distribution functions and the parameters on which GOSs are based, to establish Shaked-Shanthikumar multivariate dispersive ordering of GOSs from one sample and Khaledi-Kochar multivariate dispersive ordering of GOSs from two samples. Some applications are also given.

Ordering Conditional Distributions of Spacings of Generalized Order Statistics

2007

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.