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.

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].

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.

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 On the quotient moment of lower generalized order statistics and characterization

2015 ◽  
Vol 11 (1) ◽  
pp. 73-89
Author(s):  
Devendra Kumar
Keyword(s):  
Order Statistics ◽  
Recurrence Relation ◽  
Conditional Expectation ◽  
General Class ◽  
Recurrence Relations ◽  
Generalized Order Statistics ◽  
Lower Records ◽  
Moments Of Order Statistics ◽  
Generalized Order

Abstract In this paper we consider general class of distribution. Recurrence relations satisfied by the quotient moments and conditional quotient moments of lower generalized order statistics for a general class of distribution are derived. Further the results are deduced for quotient moments of order statistics and lower records and characterization of this distribution by considering the recurrence relation of conditional expectation for general class of distribution satisfied by the quotient moment of the lower generalized order statistics.

Likelihood ratio comparisons and logconvexity properties of p-spacings from generalized order statistics

2021 ◽  
pp. 1-20
Author(s):  
Mahdi Alimohammadi ◽  
Maryam Esna-Ashari ◽  
Jorge Navarro
Keyword(s):  
Order Statistics ◽  
Likelihood Ratio ◽  
Record Values ◽  
Generalized Order Statistics ◽  
Model Parameters ◽  
Stochastic Comparisons ◽  
Sequential Order Statistics ◽  
Progressive Type ◽  
Likelihood Ratio Ordering ◽  
Generalized Order

Due to the importance of generalized order statistics (GOS) in many branches of Statistics, a wide interest has been shown in investigating stochastic comparisons of GOS. In this article, we study the likelihood ratio ordering of $p$ -spacings of GOS, establishing some flexible and applicable results. We also settle certain unresolved related problems by providing some useful lemmas. Since we do not impose restrictions on the model parameters (as previous studies did), our findings yield new results for comparison of various useful models of ordered random variables including order statistics, sequential order statistics, $k$ -record values, Pfeifer's record values, and progressive Type-II censored order statistics with arbitrary censoring plans. Some results on preservation of logconvexity properties among spacings are provided as well.

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.

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