Fractional cumulative residual Kullback-Leibler information based on Tsallis entropy

2020 ◽  
Vol 139 ◽  
pp. 110292
Author(s):  
Xuegeng Mao ◽  
Pengjian Shang ◽  
Jianing Wang ◽  
Yi Yin
Keyword(s):  
Tsallis Entropy ◽  
Leibler Information ◽  
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 Goodness of Fit Tests for the Log-Logistic Distribution Based on Cumulative Entropy under Progressive Type II Censoring

Mathematics ◽  
2019 ◽  
Vol 7 (4) ◽  
pp. 361 ◽  
Author(s):  
Yuge Du ◽  
Wenhao Gui
Keyword(s):  
Goodness Of Fit ◽  
Likelihood Estimation ◽  
Logistic Distribution ◽  
Type Ii ◽  
Type Ii Censoring ◽  
Goodness Of Fit Tests ◽  
Progressive Type ◽  
Leibler Information ◽  
Cumulative Residual ◽  
Progressive Type Ii Censoring

In this paper, we propose two new methods to perform goodness-of-fit tests on the log-logistic distribution under progressive Type II censoring based on the cumulative residual Kullback-Leibler information and cumulative Kullback-Leibler information. Maximum likelihood estimation and the EM algorithm are used for statistical inference of the unknown parameter. The Monte Carlo simulation is conducted to study the power analysis on the alternative distributions of the hazard function monotonically increasing and decreasing. Finally, we present illustrative examples to show the applicability of the proposed methods.

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.

On cumulative residual Kullback–Leibler information

2012 ◽  
Vol 82 (11) ◽  
pp. 2025-2032 ◽  
Author(s):  
Sangun Park ◽  
Murali Rao ◽  
Dong Wan Shin
Keyword(s):  
Leibler Information ◽  
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
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