Sign in to use this feature.

Years

Between: -

Subjects

remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline

Journals

Article Types

Countries / Regions

Search Results (6)

Search Parameters:
Keywords = empirical extropy

Order results
Result details
Results per page
Select all
Export citation of selected articles as:
26 pages, 575 KB  
Article
Generalizing Uncertainty Through Dynamic Development and Analysis of Residual Cumulative Generalized Fractional Extropy with Applications in Human Health
by Mohamed Said Mohamed and Hanan H. Sakr
Fractal Fract. 2025, 9(6), 388; https://doi.org/10.3390/fractalfract9060388 - 17 Jun 2025
Cited by 1 | Viewed by 402
Abstract
The complementary dual of entropy has received significant attention in the literature. Due to the emergence of many generalizations and extensions of entropy, the need to generalize the complementary dual of uncertainty arose. This article develops the residual cumulative generalized fractional extropy as [...] Read more.
The complementary dual of entropy has received significant attention in the literature. Due to the emergence of many generalizations and extensions of entropy, the need to generalize the complementary dual of uncertainty arose. This article develops the residual cumulative generalized fractional extropy as a generalization of the residual cumulative complementary dual of entropy. Many properties, including convergence, transformation, bounds, recurrence relations, and connections with other measures, are discussed. Moreover, the proposed measure’s order statistics and stochastic order are examined. Furthermore, the dynamic design of the measure, its properties, and its characterization are considered. Finally, nonparametric estimation via empirical residual cumulative generalized fractional extropy with an application to blood transfusion is performed. Full article
Show Figures

Figure 1

13 pages, 327 KB  
Article
Estimation of Weighted Extropy with Focus on Its Use in Reliability Modeling
by Muhammed Rasheed Irshad, Krishnakumar Archana, Radhakumari Maya and Maria Longobardi
Entropy 2024, 26(2), 160; https://doi.org/10.3390/e26020160 - 11 Feb 2024
Cited by 2 | Viewed by 1593
Abstract
In the literature, estimation of weighted extropy is infrequently considered. In this paper, some non-parametric estimators of weighted extropy are given. The validation and comparison of the estimators are implemented with the help of simulation study and data illustration. The usefulness of the [...] Read more.
In the literature, estimation of weighted extropy is infrequently considered. In this paper, some non-parametric estimators of weighted extropy are given. The validation and comparison of the estimators are implemented with the help of simulation study and data illustration. The usefulness of the estimators is demonstrated using real data sets. Full article
(This article belongs to the Section Information Theory, Probability and Statistics)
Show Figures

Figure 1

25 pages, 664 KB  
Article
Extropy and Some of Its More Recent Related Measures for Concomitants of K-Record Values in an Extended FGM Family
by Mohamed A. Abd Elgawad, Haroon M. Barakat, Metwally A. Alawady, Doaa A. Abd El-Rahman, Islam A. Husseiny, Atef F. Hashem and Naif Alotaibi
Mathematics 2023, 11(24), 4934; https://doi.org/10.3390/math11244934 - 12 Dec 2023
Cited by 5 | Viewed by 1221
Abstract
This study uses an effective, recently extended Farlie–Gumbel–Morgenstern (EFGM) family to derive the distribution of concomitants of K-record upper values (CKRV). For this CKRV, the negative cumulative residual extropy (NCREX), weighted NCREX (WNCREX), negative cumulative extropy (NCEX), and weighted NCEX (WNCEX) are [...] Read more.
This study uses an effective, recently extended Farlie–Gumbel–Morgenstern (EFGM) family to derive the distribution of concomitants of K-record upper values (CKRV). For this CKRV, the negative cumulative residual extropy (NCREX), weighted NCREX (WNCREX), negative cumulative extropy (NCEX), and weighted NCEX (WNCEX) are theoretically and numerically examined. This study presents several beautiful symmetrical and asymmetric relationships that these inaccuracy measurements satisfy. Additionally, empirical estimations are provided for these measures, and their visualizations enable users to verify their accuracy. Full article
(This article belongs to the Special Issue Probability, Statistics & Symmetry)
Show Figures

Figure 1

19 pages, 548 KB  
Article
Extropy Based on Concomitants of Order Statistics in Farlie-Gumbel-Morgenstern Family for Random Variables Representing Past Life
by Muhammed Rasheed Irshad, Krishnakumar Archana, Amer Ibrahim Al-Omari, Radhakumari Maya and Ghadah Alomani
Axioms 2023, 12(8), 792; https://doi.org/10.3390/axioms12080792 - 16 Aug 2023
Cited by 4 | Viewed by 1447
Abstract
In this paper, we refined the concept of past extropy measure for concomitants of order statistics from Farlie-Gumbel-Morgenstern family. In addition, cumulative past extropy measure and dynamic cumulative past extropy measure for concomitant of rth order statistic are also conferred and their [...] Read more.
In this paper, we refined the concept of past extropy measure for concomitants of order statistics from Farlie-Gumbel-Morgenstern family. In addition, cumulative past extropy measure and dynamic cumulative past extropy measure for concomitant of rth order statistic are also conferred and their properties are studied. The problem of estimating the cumulative past extropy is investigated using empirical technique. The validity of the proposed estimator has been emphasized using simulation study. Full article
Show Figures

Figure 1

17 pages, 553 KB  
Article
Measures of Extropy Based on Concomitants of Generalized Order Statistics under a General Framework from Iterated Morgenstern Family
by Islam A. Husseiny, Metwally A. Alawady, Salem A. Alyami and Mohamed A. Abd Elgawad
Mathematics 2023, 11(6), 1377; https://doi.org/10.3390/math11061377 - 12 Mar 2023
Cited by 7 | Viewed by 1706
Abstract
In this work, we reveal some distributional characteristics of concomitants of generalized order statistics (GOS) with parameters that are pairwise different, arising from iterated Farlie–Gumbel–Morgenstern (IFGM) family of bivariate distributions. Additionally, the joint distribution and product moments of concomitants of GOS for this [...] Read more.
In this work, we reveal some distributional characteristics of concomitants of generalized order statistics (GOS) with parameters that are pairwise different, arising from iterated Farlie–Gumbel–Morgenstern (IFGM) family of bivariate distributions. Additionally, the joint distribution and product moments of concomitants of GOS for this family are discussed. Moreover, some well-known information measures, i.e., extropy, cumulative residual extropy (CRJ), and negative cumulative extropy (NCJ), are derived. Applications of these results are given for order statistics, record values, and progressive type-II censored order statistics with uniform marginals distributions. Additionally, the issue of estimating the CRJ and NCJ is looked into, utilizing the empirical technique and the concomitant of GOS. Finally, bivariate real-world data sets have been analyzed for illustrative purposes, and the performance of the proposed method is quite satisfactory. Full article
(This article belongs to the Section D1: Probability and Statistics)
Show Figures

Figure 1

12 pages, 325 KB  
Article
Weighted Cumulative Past Extropy and Its Inference
by Mohammad Reza Kazemi, Majid Hashempour and Maria Longobardi
Entropy 2022, 24(10), 1444; https://doi.org/10.3390/e24101444 - 11 Oct 2022
Cited by 9 | Viewed by 2066
Abstract
This paper introduces and studies a new generalization of cumulative past extropy called weighted cumulative past extropy (WCPJ) for continuous random variables. We explore the following: if the WCPJs of the last order statistic are equal for two distributions, then these two distributions [...] Read more.
This paper introduces and studies a new generalization of cumulative past extropy called weighted cumulative past extropy (WCPJ) for continuous random variables. We explore the following: if the WCPJs of the last order statistic are equal for two distributions, then these two distributions will be equal. We examine some properties of the WCPJ, and a number of inequalities involving bounds for WCPJ are obtained. Studies related to reliability theory are discussed. Finally, the empirical version of the WCPJ is considered, and a test statistic is proposed. The critical cutoff points of the test statistic are computed numerically. Then, the power of this test is compared to a number of alternative approaches. In some situations, its power is superior to the rest, and in some other settings, it is somewhat weaker than the others. The simulation study shows that the use of this test statistic can be satisfactory with due attention to its simple form and the rich information content behind it. Full article
(This article belongs to the Special Issue Measures of Information II)
Show Figures

Figure 1

Back to TopTop