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 Some Results on Quantile-based Dynamic Survival and Failure Tsallis Entropy

2021 ◽  
Vol 53 ◽  
Author(s):  
Vikas Kumar ◽  
Rekha Rani ◽  
Nirdesh Singh
Keyword(s):  
Tsallis Entropy ◽  
Entropy Measure ◽  
Entropy Measures

Non-additive entropy measures are important for many applications. In this paper, we introduce a quantile-based non-additive entropy measure, based on Tsallis entropy and study their properties. Some relationships of this measure with well-known reliability mea- sures and ageing classes are studied and some characterization results are presented. Also the concept of quantile-based shift independent entropy measures has been introduced and studied various properties.

scholarly journals 𝑯𝑵- Entropy: A New Measureof Information And Its Properties

2022 ◽  
Vol 24 (1) ◽  
pp. 105-118
Author(s):  
Mervat Mahdy ◽  
◽  
Dina S. Eltelbany ◽  
Hoda Mohammed ◽  
◽  
...  
Keyword(s):  
Information Theory ◽  
Shannon Entropy ◽  
Basic Concept ◽  
Random Quantity ◽  
Numerical Results ◽  
Alternative Measure ◽  
Weighted Version ◽  
Amount Of Information ◽  
Entropy Measures ◽  
Cumulative Residual

Entropy measures the amount of uncertainty and dispersion of an unknown or random quantity, this concept introduced at first by Shannon (1948), it is important for studies in many areas. Like, information theory: entropy measures the amount of information in each message received, physics: entropy is the basic concept that measures the disorder of the thermodynamical system, and others. Then, in this paper, we introduce an alternative measure of entropy, called 𝐻𝑁- entropy, unlike Shannon entropy, this proposed measure of order α and β is more flexible than Shannon. Then, the cumulative residual 𝐻𝑁- entropy, cumulative 𝐻𝑁- entropy, and weighted version have been introduced. Finally, comparison between Shannon entropy and 𝐻𝑁- entropy and numerical results have been introduced.

Point Set Registration Using Havrda–Charvat–Tsallis Entropy Measures

2011 ◽  
Vol 30 (2) ◽  
pp. 451-460 ◽  
Author(s):  
Nicholas J Tustison ◽  
Suyash P Awate ◽  
Gang Song ◽  
Tessa S Cook ◽  
James C Gee
Keyword(s):  
Tsallis Entropy ◽  
Point Set Registration ◽  
Entropy Measures ◽  
Point Set

On Rényi entropies of order statistics

2015 ◽  
Vol 08 (06) ◽  
pp. 1550080 ◽  
Author(s):  
Richa Thapliyal ◽  
H. C. Taneja
Keyword(s):  
Distribution Function ◽  
Sequence Analysis ◽  
Order Statistics ◽  
Dna Sequence ◽  
Dna Sequences ◽  
Biological Systems ◽  
Dna Sequence Analysis ◽  
Entropy Measure ◽  
Entropy Measures ◽  
Cumulative Residual

In this paper we consider a generalize dynamic entropy measure and prove that this measure characterizes the distribution function uniquely. Also we propose cumulative residual Rényi entropy of order statistics and prove that it also determines the distribution function uniquely. Applications of entropy concepts to DNA sequence analysis, the ultimate support for the biological systems, have been widely explored by researchers. The entropy measures discussed here can be applied for analysis of ordered DNA sequences.

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 Fractional Entropy-Based Test of Uniformity with Power Comparisons

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Mohamed S. Mohamed ◽  
Haroon M. Barakat ◽  
Salem A. Alyami ◽  
Mohamed A. Abd Elgawad
Keyword(s):  
Simulation Study ◽  
Limit Distribution ◽  
Residual Entropy ◽  
Test Statistic ◽  
Percentage Points ◽  
Entropy Measures ◽  
Cumulative Residual Entropy ◽  
Power Comparisons ◽  
Fractional Entropy ◽  
Cumulative Residual

In the present paper, we use the fractional and weighted cumulative residual entropy measures to test the uniformity. The limit distribution and an approximation of the distribution of the test statistic based on the fractional cumulative residual entropy are derived. Moreover, for this test statistic, percentage points and power against seven alternatives are reported. Finally, a simulation study is carried out to compare the power of the proposed tests and other tests of uniformity.

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