scholarly journals Bayesian Estimation and Prediction for Exponentiated Generalized Inverted Kumaraswamy Distribution Based on Dual Generalized Order Statistics

2021 ◽  
pp. 94-111
Author(s):  
A. M. Abd Al-Fattah ◽  
R. E. Abd El-Kader ◽  
A. A. El-Helbawy ◽  
G. R. Al-Dayian
Keyword(s):  
Order Statistics ◽  
Loss Function ◽  
Hazard Rate ◽  
Numerical Study ◽  
Generalized Order Statistics ◽  
Squared Error Loss Function ◽  
Kumaraswamy Distribution ◽  
Rate Functions ◽  
Dual Generalized Order Statistics ◽  
Generalized Order

In this paper, the shape parameters, reliability and hazard rate functions of the exponentiated generalized inverted Kumaraswamy distribution are estimated using Bayesian approach. The Bayes estimators are derived under the squared error loss function and the linear-exponential loss function based on dual generalized order statistics. Credible intervals for the parameters, reliability and hazard rate functions are obtained. The Bayesian prediction (point and interval) for a future observation of the exponentiated generalized inverted Kumaraswamy distribution is obtained based on dual generalized order statistics. All results are specialized to lower record values and a numerical study is presented. Moreover, the theoretical results are applied on three real data sets.

scholarly journals Statistical Inference for Inverted Kumaraswamy Distribution Based on Dual Generalized Order Statistics

2020 ◽  
pp. 649-660
Author(s):  
Abeer Abd-Alla EL-Helbawy ◽  
Gannat Ramadan AL-Dayian ◽  
Asmaa Mohamed Abd AL-Fattah
Keyword(s):  
Order Statistics ◽  
Loss Function ◽  
Hazard Rate ◽  
Numerical Study ◽  
Generalized Order Statistics ◽  
Squared Error Loss Function ◽  
Kumaraswamy Distribution ◽  
Rate Functions ◽  
Dual Generalized Order Statistics ◽  
Generalized Order

In this paper, the shape parameters, reliability and hazard rate functions of the inverted Kumaraswamy distribution are estimated using maximum likelihood and Bayesian methods based on dual generalized order statistics. The Bayes estimators are derived under the squared error loss function as a symmetric loss function and the linear-exponential loss function as an asymmetric loss function based on dual generalized order statistics. Confidence and credible intervals for the parameters, reliability and hazard rate functions are obtained. All results are specialized to lower record values, also a numerical study is presented to illustrate the theoretical procedures.

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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