Tsallis Entropy Measures for Concomitants of Generalized Order Statistics with Applications in Image Segmentation and Reliability Analysis
This paper develops a general framework for Tsallis entropy (TsE) and cumulative residual Tsallis entropy (CRTsE) for concomitants of generalized order statistics under the Cambanis family of bivariate distributions. Explicit closed-form expressions and alternative representations for TsE and its cumulative residual counterparts, including a unique formulation of the alternative CRTsE, are derived. Various structural properties are established, including symmetry relations between low- and high-rank concomitants, as well as connections with classical submodels such as order statistics and record values. A nonparametric estimator for the CRTsE is proposed; its mean, variance, and consistency properties are investigated analytically and through extensive Monte Carlo simulations. The theoretical framework is further illustrated through two application domains: reliability assessment of real bivariate system data, and histogram-based image segmentation via a rank-sensitive Tsallis-thresholding scheme. The proposed methodology constitutes a flexible, dependence-aware generalization of classical Shannon-based entropy measures and is particularly advantageous for systems exhibiting nonlinear dependence, tail sensitivity, or non-extensive behavior.
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This paper develops a general framework for Tsallis entropy (TsE) and cumulative residual Tsallis entropy (CRTsE) for concomitants of generalized order statistics under the Cambanis family of…
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