Characterization of symmetric distributions based on some information measures properties of order statistics

2019 ◽  
Vol 517 ◽  
pp. 141-152 ◽  
Author(s):  
J. Ahmadi ◽  
M. Fashandi
Keyword(s):  
Order Statistics ◽  
Symmetric Distributions ◽  
Information Measures

scholarly journals Characterization of symmetric distributions based on concomitants of ordered variables from FGMs family of bivariate distributions

Filomat ◽  
2019 ◽  
Vol 33 (13) ◽  
pp. 4239-4250 ◽  
Author(s):  
Jafar Ahmadi ◽  
M. Fashandi
Keyword(s):  
Order Statistics ◽  
Lower Order ◽  
Symmetric Distribution ◽  
Bivariate Distributions ◽  
Symmetric Distributions ◽  
Concomitants Of Order Statistics ◽  
Distribution Moments

Several characterization results of a symmetric distribution based on concomitants of order statistics as well as k-records from Farlie-Gumbel-Morgenstern (FGM) family of bivariate distributions are established. These include characterizations of a symmetric distribution on the basis of equality in distribution, moments, R?nyi and Tsallis entropies of concomitants of upper and lower order statistics, also in terms of the same properties of concomitants of upper and lower k-records.

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.

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.

scholarly journals SPATIOTEMPORAL CHAOS, LOCALIZED STRUCTURES AND SYNCHRONIZATION IN THE VECTOR COMPLEX GINZBURG–LANDAU EQUATION

1999 ◽  
Vol 09 (12) ◽  
pp. 2257-2264 ◽  
Author(s):  
EMILIO HERNÁNDEZ-GARCÍA ◽  
MIGUEL HOYUELOS ◽  
PERE COLET ◽  
MAXI SAN MIGUEL ◽  
RAÚL MONTAGNE
Keyword(s):  
Chaotic Dynamics ◽  
Landau Equation ◽  
Spatiotemporal Chaos ◽  
Quantitative Characterization ◽  
Ginzburg Landau ◽  
Information Measures ◽  
Localized Structures ◽  
Ginzburg Landau Equation ◽  
Spatial Dimensions

We study the spatiotemporal dynamics, in one and two spatial dimensions, of two complex fields which are the two components of a vector field satisfying a vector form of the complex Ginzburg–Landau equation. We find synchronization and generalized synchronization of the spatiotemporally chaotic dynamics. The two kinds of synchronization can coexist simultaneously in different regions of the space, and they are mediated by localized structures. A quantitative characterization of the degree of synchronization is given in terms of mutual information measures.

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