scholarly journals Estimation of the Parameters of Burr Type III Distribution Based on Dual Generalized Order Statistics

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Chansoo Kim ◽  
Woosuk Kim
Keyword(s):  
Maximum Likelihood ◽  
Order Statistics ◽  
Information Matrix ◽  
Exact Expression ◽  
Bayes Estimator ◽  
Generalized Order Statistics ◽  
Monte Carlo Simulation Study ◽  
Type Iii ◽  
Dual Generalized Order Statistics ◽  
Generalized Order

The estimation of the parameters of Burr type III distribution based on dual generalized order statistics is considered by using the maximum likelihood (ML) approach as well as the Bayesian approach. The exact expression of the expected Fisher information matrix of the parameters in the distribution is obtained. Also, an approximation based on Lindley is used to obtain the Bayes estimator. To compare the maximum likelihood estimator and the Bayes estimator of the parameters, Monte Carlo simulation study is performed.

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.

Limit theory of bivariate dual generalized order statistics with random index

Statistics ◽  
2016 ◽  
Vol 51 (3) ◽  
pp. 572-590 ◽  
Author(s):  
M. A. Abd Elgawad ◽  
H. M. Barakat ◽  
Hong Qin ◽  
Ting Yan
Keyword(s):  
Order Statistics ◽  
Generalized Order Statistics ◽  
Limit Theory ◽  
Random Index ◽  
Dual Generalized Order Statistics ◽  
Generalized Order
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