Generalizing Uncertainty Through Dynamic Development and Analysis of Residual Cumulative Generalized Fractional Extropy with Applications in Human Health
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 ext...
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MDPI AG
2025-06-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/9/6/388 |
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| author | Mohamed Said Mohamed Hanan H. Sakr |
| author_facet | Mohamed Said Mohamed Hanan H. Sakr |
| author_sort | Mohamed Said Mohamed |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-cda2b0c4c273433e9be394da9160daf6 |
| institution | Kabale University |
| issn | 2504-3110 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj-art-cda2b0c4c273433e9be394da9160daf62025-08-20T03:24:36ZengMDPI AGFractal and Fractional2504-31102025-06-019638810.3390/fractalfract9060388Generalizing Uncertainty Through Dynamic Development and Analysis of Residual Cumulative Generalized Fractional Extropy with Applications in Human HealthMohamed Said Mohamed0Hanan H. Sakr1Department of Mathematics, Faculty of Education, Ain Shams University, Cairo 11341, EgyptDepartment of Management Information Systems, College of Business Administration in Hawtat Bani Tamim, Prince Sattam Bin Abdulaziz University, Saudi ArabiaThe 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.https://www.mdpi.com/2504-3110/9/6/388distorted stop-loss transformmean residual life functionnonparametric estimationorder statisticsresidual cumulative entropystochastic comparison |
| spellingShingle | Mohamed Said Mohamed Hanan H. Sakr Generalizing Uncertainty Through Dynamic Development and Analysis of Residual Cumulative Generalized Fractional Extropy with Applications in Human Health Fractal and Fractional distorted stop-loss transform mean residual life function nonparametric estimation order statistics residual cumulative entropy stochastic comparison |
| title | Generalizing Uncertainty Through Dynamic Development and Analysis of Residual Cumulative Generalized Fractional Extropy with Applications in Human Health |
| title_full | Generalizing Uncertainty Through Dynamic Development and Analysis of Residual Cumulative Generalized Fractional Extropy with Applications in Human Health |
| title_fullStr | Generalizing Uncertainty Through Dynamic Development and Analysis of Residual Cumulative Generalized Fractional Extropy with Applications in Human Health |
| title_full_unstemmed | Generalizing Uncertainty Through Dynamic Development and Analysis of Residual Cumulative Generalized Fractional Extropy with Applications in Human Health |
| title_short | Generalizing Uncertainty Through Dynamic Development and Analysis of Residual Cumulative Generalized Fractional Extropy with Applications in Human Health |
| title_sort | generalizing uncertainty through dynamic development and analysis of residual cumulative generalized fractional extropy with applications in human health |
| topic | distorted stop-loss transform mean residual life function nonparametric estimation order statistics residual cumulative entropy stochastic comparison |
| url | https://www.mdpi.com/2504-3110/9/6/388 |
| work_keys_str_mv | AT mohamedsaidmohamed generalizinguncertaintythroughdynamicdevelopmentandanalysisofresidualcumulativegeneralizedfractionalextropywithapplicationsinhumanhealth AT hananhsakr generalizinguncertaintythroughdynamicdevelopmentandanalysisofresidualcumulativegeneralizedfractionalextropywithapplicationsinhumanhealth |