scholarly journals Residual and Past Entropy for Concomitants of Ordered Random Variables of Morgenstern Family

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
M. M. Mohie EL-Din ◽  
M. M. Amein ◽  
Nahed S. A. Ali ◽  
M. S. Mohamed
Keyword(s):  
Order Statistics ◽  
Linear Transformation ◽  
Random Variables ◽  
Generalized Order Statistics ◽  
The Past ◽  
Different Types ◽  
Past Entropy ◽  
Past Life ◽  
Family Based ◽  
Generalized Order

For a system, which is observed at timet, the residual and past entropies measure the uncertainty about the remaining and the past life of the distribution, respectively. In this paper, we have presented the residual and past entropy of Morgenstern family based on the concomitants of the different types of generalized order statistics (gos) and give the linear transformation of such model. Characterization results for these dynamic entropies for concomitants of ordered random variables have been considered.

scholarly journals On concomitants of ordered random variables under general forms of Morgenstern family

Filomat ◽  
2019 ◽  
Vol 33 (9) ◽  
pp. 2771-2780
Author(s):  
Mohamed Mohamed
Keyword(s):  
Order Statistics ◽  
Shannon Entropy ◽  
Random Variables ◽  
Generalized Order Statistics ◽  
Unified Approach ◽  
Leibler Divergence ◽  
Different Types ◽  
Dual Generalized Order Statistics ◽  
Generalized Order

Based on the extensions of Morgenstern family (Huang and Bairamov extensions), the concomitants of different types of generalized order statistics (gos) and dual generalized order statistics (dgos) are obtained. Moreover, a unified approach to such models is derived. Information properties such as Shannon entropy and Kullback-Leibler divergence for Huang and Kotz extension are obtained.

ORDERING CONDITIONAL DISTRIBUTIONS OF GENERALIZED ORDER STATISTICS

2007 ◽  
Vol 21 (3) ◽  
pp. 401-417 ◽  
Author(s):  
Taizhong Hu ◽  
Wei Jin ◽  
Baha-Eldin Khaledi
Keyword(s):  
Order Statistics ◽  
Likelihood Ratio ◽  
Random Variables ◽  
Generalized Order Statistics ◽  
Conditional Distributions ◽  
Unified Approach ◽  
Two Samples ◽  
Generalized Order

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 [17]. Some applications of the main results are also given.

NONNEGATIVITY OF COVARIANCES BETWEEN FUNCTIONS OF ORDERED RANDOM VARIABLES

2007 ◽  
Vol 21 (4) ◽  
pp. 557-577 ◽  
Author(s):  
Taizhong Hu ◽  
Junchao Yao ◽  
Qingshu Lu
Keyword(s):  
Order Statistics ◽  
Random Variables ◽  
Random Variable ◽  
Record Values ◽  
Poisson Processes ◽  
Generalized Order Statistics ◽  
Geometric Processes ◽  
Unified Method ◽  
Generalized Order

In this article we investigate conditions by a unified method under which the covariances of functions of two adjacent ordered random variables are nonnegative. The main structural results are applied to several kinds of ordered random variable, such as delayed record values, continuous and discrete ℓ∞⩽-spherical order statistics, epoch times of mixed Poisson processes, generalized order statistics, discrete weak record values, and epoch times of modified geometric processes. These applications extend the main results for ordinary order statistics in Qi [28] and for usual record values in Nagaraja and Nevzorov [25].

STOCHASTIC ORDERINGS BETWEEN p-SPACINGS OF GENERALIZED ORDER STATISTICS FROM TWO SAMPLES

2006 ◽  
Vol 20 (3) ◽  
pp. 465-479 ◽  
Author(s):  
Taizhong Hu ◽  
Weiwei Zhuang
Keyword(s):  
Order Statistics ◽  
Likelihood Ratio ◽  
Hazard Rate ◽  
Random Variables ◽  
Generalized Order Statistics ◽  
Unified Approach ◽  
Stochastic Orderings ◽  
Two Samples ◽  
Likelihood Ratio Ordering ◽  
Generalized Order

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 investigate conditions on the distributions and the parameters on which the generalized order statistics are based to establish the likelihood ratio ordering of general p-spacings and the hazard rate and the dispersive orderings of (normalizing) simple spacings from two samples. We thus strengthen and complement some results in Franco, Ruiz, and Ruiz [7] and Belzunce, Mercader, and Ruiz [5]. This article is a continuation of Hu and Zhuang [10].

SOME NEW RESULTS ON ORDERING OF SIMPLE SPACINGS OF GENERALIZED ORDER STATISTICS

2010 ◽  
Vol 25 (1) ◽  
pp. 71-81 ◽  
Author(s):  
Hongmei Xie ◽  
Weiwei Zhuang
Keyword(s):  
Order Statistics ◽  
Residual Life ◽  
Random Variables ◽  
Generalized Order Statistics ◽  
Mean Residual Life ◽  
Unified Approach ◽  
Stochastic Comparisons ◽  
The Mean ◽  
Generalized Order

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 several stochastic comparisons of simple spacings in the mean residual life and the excess wealth orders under the more general assumptions on the parameters of the models.

FURTHER RESULTS ON QUANTILE ENTROPY IN THE PAST LIFETIME

2018 ◽  
Vol 33 (1) ◽  
pp. 146-159 ◽  
Author(s):  
Guoxin Qiu
Keyword(s):  
Order Statistics ◽  
Sufficient Conditions ◽  
Random Variable ◽  
Generalized Order Statistics ◽  
Closure Properties ◽  
The Past ◽  
Inactivity Time ◽  
Generalized Order

Bounds of the quantile entropy in the past lifetime of some ageing classes are explored firstly. The quantile entropy in the past lifetime of a random variable is shown to be increasing if its expected inactivity time is increasing. Some closure properties of the less quantile entropy in the past lifetime order are obtained under the model of generalized order statistics. Moreover, sufficient conditions are given for a function of a random variable and for a weighted random variable to have more quantile entropy in the past lifetime than original random variable.

STOCHASTIC PROPERTIES OF p-SPACINGS OF GENERALIZED ORDER STATISTICS

2005 ◽  
Vol 19 (2) ◽  
pp. 257-276 ◽  
Author(s):  
Taizhong Hu ◽  
Weiwei Zhuang
Keyword(s):  
Order Statistics ◽  
Likelihood Ratio ◽  
Hazard Rate ◽  
Random Variables ◽  
Generalized Order Statistics ◽  
Unified Approach ◽  
Stochastic Comparisons ◽  
Stochastic Properties ◽  
Generalized Order

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 investigate the conditions on the parameters that enable one to establish several stochastic comparisons of general p-spacings for a subclass of generalized order statistics in the likelihood ratio and the hazard rate orders. Preservation properties of the logconvexity and logconcavity of p-spacings are also given.

scholarly journals A measure of inaccuracy in concomitants of ordered random variables under Farlie-Gumbel-Morgenstern family

Filomat ◽  
2019 ◽  
Vol 33 (15) ◽  
pp. 4931-4942
Author(s):  
Mohamed Mohamed
Keyword(s):  
Distribution Function ◽  
Order Statistics ◽  
Communication Theory ◽  
Random Variables ◽  
Random Variable ◽  
Generalized Order Statistics ◽  
Stochastic Comparisons ◽  
Vague Statement ◽  
Generalized Order

In communication theory, for possible outcomes of an experiment, we have two basic problems for the statement of the experimenter: we may not have enough information (vague statement) or some of the information may be incorrect, which make inaccurate in either or both of these situations. In this article, a measure of inaccuracy and its residual between distributions of concomitants of generalized order statistics (1os) and parent random variable are extended. Results of inaccuracy for family distributions and stochastic comparisons are obtained. Furthermore, some properties of the proposed measure are discussed. The unique characterization of the distribution function of parent random variable by the inaccuracy is shown.

scholarly journals The extended generalized half logistic distribution based on ordered random variables

2015 ◽  
Vol 46 (3) ◽  
pp. 245-256 ◽  
Author(s):  
Devendra Kumar
Keyword(s):  
Order Statistics ◽  
Generating Functions ◽  
Conditional Expectation ◽  
Recurrence Relations ◽  
Random Variables ◽  
Record Values ◽  
Joint Moment ◽  
Generalized Order Statistics ◽  
Logistic Distribution ◽  
Generalized Order

In this paper, we considered an extended generalized half logistic distribution and derived some explicit expressions and recurrence relations for marginal and joint moment generating functions of generalized order statistics from extended generalized half logistic distribution. The results for record values and order statistics are deduced from the result. Finally, we obtained the characterizing result of this distribution on using the conditional expectation of generalized order statistics.

scholarly journals Information Measures for Generalized Order Statistics and Their Concomitants under General Framework from Huang-Kotz FGM Bivariate Distribution

Entropy ◽  
2021 ◽  
Vol 23 (3) ◽  
pp. 335
Author(s):  
Mohamed A. Abd Elgawad ◽  
Haroon M. Barakat ◽  
Shengwu Xiong ◽  
Salem A. Alyami
Keyword(s):  
Order Statistics ◽  
General Framework ◽  
Bivariate Distribution ◽  
Generalized Order Statistics ◽  
Information Measures ◽  
Progressive Type ◽  
Information Number ◽  
Fisher Information Number ◽  
Dual Generalized Order Statistics ◽  
Generalized Order

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, such as the progressive type-II censored order statistics.

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