Some new results on multivariate dispersive ordering of generalized order statistics (original) (raw)
Entropy
In this paper, we study the concomitants of dual generalized order statistics (and consequently generalized order statistics) when the parameters γ1,…,γn are assumed to be pairwise different from Huang–Kotz Farlie–Gumble–Morgenstern bivariate distribution. Some useful recurrence relations between single and product moments of concomitants are obtained. Moreover, Shannon’s entropy and the Fisher information number measures are derived. Finally, these measures are extensively studied for some well-known distributions such as exponential, Pareto and power distributions. The main motivation of the study of the concomitants of generalized order statistics (as an important practical kind to order the bivariate data) under this general framework is to enable researchers in different fields of statistics to use some of the important models contained in these generalized order statistics only under this general framework. These extended models are frequently used in the reliability theory, s...
Let X(1;n;m;k);X(2;n;m;k);:::;X(n;n;m;k) be n generalized order statis- tics from an absolutely continuous (with respect to Lebesgue measure) distribution. We give characterizations of distributions by means of Efˆ(X(s;n;m;k))jX(r;n;m;k) = xg = g(x) and Efˆ(X(r;n;m;k))jX(s;n;m;k) = xg = g(x);s > r under some mild conditions on ˆ(:) and g(:). It is shown that most of the known characteri- zation results based on conditional expectations are special cases of the results of this paper. 1. Introduction. Let X1;X2;:::Xn be a random sample of size n from an absolutely continuous (with respect to Lebesgue measure) distribution function (df) F(x) and the corresponding probability distribution function (pdf) f(x). We will take the support of F(x) = (fi;fl); where fi = inffx 2 IR; F(x) > 0g and fl = supfx 2 IR; F(x) < 1g: Ferguson (1967) introduced the characterization of distributions based on the linearity of regression of adjacent order statistics E(Xr+1;njXr;n = x) and its dual E...
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.
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
Moments of Generalized Order Statistics from a General Class of Distributions
2009
Order statistics, record values and several other models of ordered random variables can be viewed as special case of generalized order statistics (gos) [Kamps, 1995]. In this paper explicit expressions for single and product moments of generalized order statistics from a family of distributions have been obtained. Further, some deductions and particular cases are discussed.
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.
Journal of Statistics Applications & Probability, 2012
Distributional properties of two non-adjacent dual generalized order statistics have been used to characterize distributions. Further, one sided contraction and dilation for the dual generalized order statistics are discussed and then the results are deduced for generalized order statistics, order statistics and adjacent dual generalized order statistics and generalized order statistics
Concomitants of generalized order statistics from Farlie–Gumbel–Morgenstern distributions
Statistical Methodology, 2008
Generalized order statistics constitute a unified model for ordered random variables that includes order statistics and record values among others. Here, we consider concomitants of generalized order statistics for the Farlie-Gumbel-Morgenstern bivariate distributions and study recurrence relations between their moments. We derive the joint distribution of concomitants of two generalized order statistics and obtain their product moments. Application of these results is seen in establishing some well known results given separately for order statistics and record values and obtaining some new results.