On weighted cumulative residual Tsallis entropy and its dynamic version

2018 ◽  
Vol 491 ◽  
pp. 678-692 ◽  
Author(s):  
A.H. Khammar ◽  
S.M.A. Jahanshahi
Keyword(s):  
Tsallis Entropy ◽  
Dynamic Version ◽  
Cumulative Residual

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

Entropy ◽  
2021 ◽  
Vol 24 (1) ◽  
pp. 9
Author(s):  
Muhammed Rasheed Irshad ◽  
Radhakumari Maya ◽  
Francesco Buono ◽  
Maria Longobardi
Keyword(s):  
Numerical Evaluation ◽  
Asymptotic Properties ◽  
Kernel Estimation ◽  
Tsallis Entropy ◽  
Dependent Data ◽  
Entropy Measure ◽  
Regularity Conditions ◽  
Monte Carlo Simulation Study ◽  
Dynamic Version ◽  
Cumulative Residual

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.

scholarly journals Some Characterization Results on Dynamic Cumulative Residual Tsallis Entropy

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Madan Mohan Sati ◽  
Nitin Gupta
Keyword(s):  
Tsallis Entropy ◽  
Information Measure ◽  
Probability Models ◽  
New Information ◽  
Life Distributions ◽  
Equilibrium Probability ◽  
Dynamic Version ◽  
Cumulative Residual

We propose a generalized cumulative residual information measure based on Tsallis entropy and its dynamic version. We study the characterizations of the proposed information measure and define new classes of life distributions based on this measure. Some applications are provided in relation to weighted and equilibrium probability models. Finally the empirical cumulative Tsallis entropy is proposed to estimate the new information measure.

scholarly journals Generalized Entropies, Variance and Applications

Entropy ◽  
2020 ◽  
Vol 22 (6) ◽  
pp. 709 ◽  
Author(s):  
Abdolsaeed Toomaj ◽  
Antonio Di Crescenzo
Keyword(s):  
Residual Entropy ◽  
Dispersion Measure ◽  
Homogeneous Poisson Process ◽  
Cumulative Residual Entropy ◽  
Excess Wealth Order ◽  
Dynamic Version ◽  
Cumulative Residual ◽  
Non Homogeneous Poisson Process ◽  
Generalized Entropies ◽  
Cumulative Entropy

The generalized cumulative residual entropy is a recently defined dispersion measure. In this paper, we obtain some further results for such a measure, in relation to the generalized cumulative residual entropy and the variance of random lifetimes. We show that it has an intimate connection with the non-homogeneous Poisson process. We also get new expressions, bounds and stochastic comparisons involving such measures. Moreover, the dynamic version of the mentioned notions is studied through the residual lifetimes and suitable aging notions. In this framework we achieve some findings of interest in reliability theory, such as a characterization for the exponential distribution, various results on k-out-of-n systems, and a connection to the excess wealth order. We also obtain similar results for the generalized cumulative entropy, which is a dual measure to the generalized cumulative residual entropy.

A quantile-based study of cumulative residual Tsallis entropy measures

2018 ◽  
Vol 494 ◽  
pp. 410-421 ◽  
Author(s):  
S.M. Sunoj ◽  
Aswathy S. Krishnan ◽  
P.G. Sankaran
Keyword(s):  
Tsallis Entropy ◽  
Entropy Measures ◽  
Cumulative Residual

scholarly journals BIVARIATE DYNAMIC CUMULATIVE RESIDUAL TSALLIS ENTROPY

2017 ◽  
Vol 35 (1_2) ◽  
pp. 45-58 ◽  
Author(s):  
MADAN MOHAN SATI ◽  
HARINDER SINGH
Keyword(s):  
Tsallis Entropy ◽  
Cumulative Residual

Some Reliability Properties of Bivariate Cumulative Residual Tsallis Entropy

2020 ◽  
Vol 14 (4) ◽  
Author(s):  
David Chris Raju ◽  
S. M. Sunoj ◽  
G Rajesh
Keyword(s):  
Tsallis Entropy ◽  
Cumulative Residual
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