Measures of cumulative residual Tsallis entropy for concomitants of generalized order statistics based on the Morgenstern family with application to medical data

Ghada Mohammed Mansour; Haroon Mohamed Barakat; Islam Abdullah Husseiny; Magdy Nagy; Ahmed Hamdi Mansi; Metwally Alsayed Alawady; Ghada Mohammed Mansour; Haroon Mohamed Barakat; Islam Abdullah Husseiny; Magdy Nagy; Ahmed Hamdi Mansi; Metwally Alsayed Alawady

doi:10.3934/mbe.2025058

Mathematical Biosciences and Engineering

2025, Volume 22, Issue 6: 1572-1597. doi: 10.3934/mbe.2025058

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Research article

Measures of cumulative residual Tsallis entropy for concomitants of generalized order statistics based on the Morgenstern family with application to medical data

1.
Department of Mathematics, Faculty of Science, Zagazig University, Zagazig 44519, Egypt
2.
Department of Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
3.
Dipartimento di Ingegneria Civile e Ambientale (DICA), Politecnico di Milano, Milano 20133, Italy

Received: 07 October 2024 Revised: 07 April 2025 Accepted: 18 April 2025 Published: 15 May 2025

Ever since Tsallis introduced Tsallis entropy theory, it has been applied to a wide variety of topics in physics and chemistry, with new applications being discovered annually. The amount of research suggests that the Tsallis entropy concept holds significant potential. This paper introduces weighted cumulative residual Tsallis entropy (WCRTE) and weighted cumulative past Tsallis entropy (WCPTE), as well as their dynamic counterparts for the concomitants of $ m $-generalized order statistics ($ m $-GOSs) derived from the Farlie-Gumbel-Morgenstern bivariate family. The characteristics of the proposed entropy measures were analyzed, demonstrating their ability to characterize the Pareto and exponential distributions. Applications of these findings were presented for order statistics (OSs) systems and record values with uniform, Weibull, and power marginal distributions. Furthermore, the empirical alternatives WCRTE and WCPTE were proposed for calculating new information measures. Two real-world data sets have been evaluated for illustrative purposes, demonstrating satisfactory performance.
Citation: Ghada Mohammed Mansour, Haroon Mohamed Barakat, Islam Abdullah Husseiny, Magdy Nagy, Ahmed Hamdi Mansi, Metwally Alsayed Alawady. Measures of cumulative residual Tsallis entropy for concomitants of generalized order statistics based on the Morgenstern family with application to medical data[J]. Mathematical Biosciences and Engineering, 2025, 22(6): 1572-1597. doi: 10.3934/mbe.2025058

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Abstract

Ever since Tsallis introduced Tsallis entropy theory, it has been applied to a wide variety of topics in physics and chemistry, with new applications being discovered annually. The amount of research suggests that the Tsallis entropy concept holds significant potential. This paper introduces weighted cumulative residual Tsallis entropy (WCRTE) and weighted cumulative past Tsallis entropy (WCPTE), as well as their dynamic counterparts for the concomitants of $ m $-generalized order statistics ($ m $-GOSs) derived from the Farlie-Gumbel-Morgenstern bivariate family. The characteristics of the proposed entropy measures were analyzed, demonstrating their ability to characterize the Pareto and exponential distributions. Applications of these findings were presented for order statistics (OSs) systems and record values with uniform, Weibull, and power marginal distributions. Furthermore, the empirical alternatives WCRTE and WCPTE were proposed for calculating new information measures. Two real-world data sets have been evaluated for illustrative purposes, demonstrating satisfactory performance.

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