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

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 compu...

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Published inAIMS mathematics Vol. 9; no. 9; pp. 23268 - 23290
Main Authors Husseiny, I. A., Nagy, M., Mansi, A. H., Alawady, M. A.
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2024
Subjects
concomitants
cumulative residual tsallis entropy
generalized order statistics
ifgm family
tsallis entropy
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Summary: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.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.20241131