Kernel Estimation of Cumulative Residual Tsallis Entropy and Its Dynamic Version under ρ-Mixing Dependent Data

Entropy (Basel). 2021 Dec 21;24(1):9. doi: 10.3390/e24010009.


Tsallis introduced a non-logarithmic generalization of Shannon entropy, namely Tsallis entropy, which is non-extensive. Sati and Gupta proposed cumulative residual information based on this non-extensive entropy measure, namely cumulative residual Tsallis entropy (CRTE), and its dynamic version, namely dynamic cumulative residual Tsallis entropy (DCRTE). In the present paper, we propose non-parametric kernel type estimators for CRTE and DCRTE where the considered observations exhibit an ρ-mixing dependence condition. Asymptotic properties of the estimators were established under suitable regularity conditions. A numerical evaluation of the proposed estimator is exhibited and a Monte Carlo simulation study was carried out.

Keywords: cumulative residual Tsallis entropy; dynamic cumulative residual Tsallis entropy; kernel estimator; simulation; ρ-mixing.