Some Tsallis entropy measures in concomitants of generalized order statistics under iterated FGM bivariate distribution

I. A. Husseiny; M. Nagy; A. H. Mansi; M. A. Alawady; I. A. Husseiny; M. Nagy; A. H. Mansi; M. A. Alawady

doi:10.3934/math.20241131

AIMS Mathematics

2024, Volume 9, Issue 9: 23268-23290. doi: 10.3934/math.20241131

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Some Tsallis entropy measures in concomitants of generalized order statistics under iterated FGM bivariate distribution

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.
DICA, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133, Milano, MI, Italy

Received: 06 June 2024 Revised: 01 July 2024 Accepted: 23 July 2024 Published: 31 July 2024
MSC : 62G30, 94A17

Shannon differential entropy is extensively applied in the literature as a measure of dispersion or uncertainty. Nonetheless, there are other measurements, such as the cumulative residual Tsallis entropy (CRTE), that reveal interesting effects in several fields. Motivated by this, we study and compute Tsallis measures for the concomitants of the generalized order statistics (CGOS) from the iterated Farlie-Gumbel-Morgenstern (IFGM) bivariate family. Some newly introduced information measures are also being considered for CGOS within the framework of the IFGM family, including Tsallis entropy, CRTE, and an alternative measure of CRTE of order $ \eta $. Applications of these results are given for order statistics and record values with uniform, exponential, and power marginals distributions. In addition, the empirical cumulative Tsallis entropy is suggested as a method to calculate the new information measure. Finally, a real-world data set has been analyzed for illustrative purposes, and the performance is quite satisfactory.
- Tsallis entropy,
- cumulative residual Tsallis entropy,
- IFGM family,
- concomitants,
- generalized order statistics
Citation: I. A. Husseiny, M. Nagy, A. H. Mansi, M. A. Alawady. Some Tsallis entropy measures in concomitants of generalized order statistics under iterated FGM bivariate distribution[J]. AIMS Mathematics, 2024, 9(9): 23268-23290. doi: 10.3934/math.20241131

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Abstract

Shannon differential entropy is extensively applied in the literature as a measure of dispersion or uncertainty. Nonetheless, there are other measurements, such as the cumulative residual Tsallis entropy (CRTE), that reveal interesting effects in several fields. Motivated by this, we study and compute Tsallis measures for the concomitants of the generalized order statistics (CGOS) from the iterated Farlie-Gumbel-Morgenstern (IFGM) bivariate family. Some newly introduced information measures are also being considered for CGOS within the framework of the IFGM family, including Tsallis entropy, CRTE, and an alternative measure of CRTE of order $ \eta $. Applications of these results are given for order statistics and record values with uniform, exponential, and power marginals distributions. In addition, the empirical cumulative Tsallis entropy is suggested as a method to calculate the new information measure. Finally, a real-world data set has been analyzed for illustrative purposes, and the performance is quite satisfactory.

References

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