Irshad MR, Maya R, Buono F, Longobardi M. Kernel Estimation of Cumulative Residual Tsallis Entropy and Its Dynamic Version under
ρ-Mixing Dependent Data.
ENTROPY 2021;
24:e24010009. [PMID:
35052035 PMCID:
PMC8774551 DOI:
10.3390/e24010009]
[Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 11/19/2021] [Revised: 12/17/2021] [Accepted: 12/19/2021] [Indexed: 11/29/2022]
Abstract
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.
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