scholarly journals Ordered Variables and Their Concomitants under Extropy via COVID-19 Data Application

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Mohamed S. Mohamed ◽  
Alanazi Talal Abdulrahman ◽  
Zahra Almaspoor ◽  
M. Yusuf
Keyword(s):  
Order Statistics ◽  
Nonparametric Estimation ◽  
Upper Bound ◽  
Real Data ◽  
The Other ◽  
Generalized Order Statistics ◽  
Stochastic Orders ◽  
Other Hand ◽  
Data Application ◽  
Generalized Order

Extropy, as a complementary dual of entropy, has been discussed in many works of literature, where it is declared for other measures as an extension of extropy. In this article, we obtain the extropy of generalized order statistics via its dual and give some examples from well-known distributions. Furthermore, we study the residual and past extropy for such models. On the other hand, based on Farlie–Gumbel–Morgenstern distribution, we consider the residual extropy of concomitants of m-generalized order statistics and present this measure with some additional features. In addition, we provide the upper bound and stochastic orders of it. Finally, nonparametric estimation of the residual extropy of concomitants of m-generalized order statistics is included using simulated and real data connected with COVID-19 virus.

scholarly journals Bayesian Prediction for Exponentiated Generalized Xgamma Distribution Based on Dual Generalized Order Statistics with Application to Poverty and COVID-19 Mortality Rates

2021 ◽  
pp. 30-53
Author(s):  
R. E. Abd EL-Kader ◽  
A. M. Abd AL-Fattah ◽  
G. R. AL-Dayian ◽  
A. A. EL-Helbawy
Keyword(s):  
Order Statistics ◽  
Real Data ◽  
Generalized Order Statistics ◽  
Statistical Prediction ◽  
Data Sets ◽  
Interval Prediction ◽  
Potential Applications ◽  
Dual Generalized Order Statistics ◽  
Lower Records ◽  
Generalized Order

Statistical prediction is one of the most important problems in life testing; it has been applied in medicine, engineering, business and other areas as well. In this paper, the exponentiated generalized xgamma distribution is introduced as an application on the exponentiated generalized general class of distributions. Bayesian point and interval prediction of exponentiated generalized xgamma distribution based on dual generalized order statistics are considered. All results are specialized to lower records. The results are verified using simulation study as well as applications to real data sets to demonstrate the flexibility and potential applications of the distribution.

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.

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

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.

Limit distributions of generalized order statistics in a stationary Gaussian sequence

2017 ◽  
Vol 41 (5) ◽  
pp. 629-642
Author(s):  
E.O. Abo Zaid ◽  
H.M. Barakat ◽  
E.M. Nigm
Keyword(s):  
Order Statistics ◽  
Generalized Order Statistics ◽  
Gaussian Sequence ◽  
Stationary Gaussian Sequence ◽  
Limit Distributions ◽  
Generalized Order

scholarly journals A BOUND FOR THE INDEX OF A QUADRATIC FORM AFTER SCALAR EXTENSION TO THE FUNCTION FIELD OF A QUADRIC

2018 ◽  
Vol 19 (2) ◽  
pp. 421-450 ◽  
Author(s):  
Stephen Scully
Keyword(s):  
Quadratic Form ◽  
Upper Bound ◽  
Function Field ◽  
The Other ◽  
Direct Generalization ◽  
Other Hand ◽  
General Field ◽  
The One ◽  
Anisotropic Quadratic Form

Let $q$ be an anisotropic quadratic form defined over a general field $F$. In this article, we formulate a new upper bound for the isotropy index of $q$ after scalar extension to the function field of an arbitrary quadric. On the one hand, this bound offers a refinement of an important bound established in earlier work of Karpenko–Merkurjev and Totaro; on the other hand, it is a direct generalization of Karpenko’s theorem on the possible values of the first higher isotropy index. We prove its validity in two key cases: (i) the case where $\text{char}(F)\neq 2$, and (ii) the case where $\text{char}(F)=2$ and $q$ is quasilinear (i.e., diagonalizable). The two cases are treated separately using completely different approaches, the first being algebraic–geometric, and the second being purely algebraic.

Fisher information in generalized order statistics

Statistics ◽  
2012 ◽  
Vol 46 (6) ◽  
pp. 719-743 ◽  
Author(s):  
M. Burkschat ◽  
E. Cramer
Keyword(s):  
Order Statistics ◽  
Fisher Information ◽  
Generalized Order Statistics ◽  
Generalized Order

Random Contraction and Random Dilation of Generalized Order Statistics

2008 ◽  
Vol 37 (14) ◽  
pp. 2185-2201 ◽  
Author(s):  
Eric Beutner ◽  
Udo Kamps
Keyword(s):  
Order Statistics ◽  
Generalized Order Statistics ◽  
Generalized Order

Sharp Bounds for Generalized Order Statistics via Logarithmic Moments

2005 ◽  
Vol 34 (9-10) ◽  
pp. 1911-1923
Author(s):  
M. Kaluszka ◽  
A. Okolewski
Keyword(s):  
Order Statistics ◽  
Generalized Order Statistics ◽  
Sharp Bounds ◽  
Logarithmic Moments ◽  
Generalized Order
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