Statistical Inference for Kumaraswamy Distribution Based on Generalized Order Statistics with Applications

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.

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Statistical inference for Burr type III distribution on dual generalized order statistics and real data analysis

Applied Mathematical Sciences ◽

10.12988/ams.2016.615 ◽

2016 ◽

Vol 10 ◽

pp. 683-695 ◽

Cited By ~ 1

Author(s):

Chansoo Kim ◽

Seongho Song ◽

Woosuk Kim

Keyword(s):

Data Analysis ◽

Order Statistics ◽

Statistical Inference ◽

Real Data ◽

Generalized Order Statistics ◽

Real Data Analysis ◽

Type Iii ◽

Dual Generalized Order Statistics ◽

Generalized Order

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

Pakistan Journal of Statistics and Operation Research ◽

10.18187/pjsor.v16i4.2774 ◽

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.

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

Entropy ◽

10.3390/e23030335 ◽

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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Load-Sharing Reliability Models with Different Component Sensitivities to Other Components’ Working States

Advances in Applied Probability ◽

10.1017/apr.2020.49 ◽

2021 ◽

Vol 53 (1) ◽

pp. 107-132

Author(s):

Tomasz Rychlik ◽

Fabio Spizzichino

Keyword(s):

Order Statistics ◽

Load Sharing ◽

Single Component ◽

Generalized Order Statistics ◽

Hazard Rates ◽

System Operation ◽

Reliability Models ◽

Mixtures Of Distributions ◽

Failure Times ◽

Generalized Order

AbstractWe study the distributions of component and system lifetimes under the time-homogeneous load-sharing model, where the multivariate conditional hazard rates of working components depend only on the set of failed components, and not on their failure moments or the time elapsed from the start of system operation. Then we analyze its time-heterogeneous extension, in which the distributions of consecutive failure times, single component lifetimes, and system lifetimes coincide with mixtures of distributions of generalized order statistics. Finally we focus on some specific forms of the time-nonhomogeneous load-sharing model.

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