A quantile-based study of cumulative residual Tsallis entropy measures

Sunoj, S. M.; Krishnan, Aswathy S.; Sankaran, P. G.

doi:10.1016/j.physa.2017.12.058

Cited by 14 publications

(6 citation statements)

References 22 publications

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“…The reader can find other results and applications concerning the Kaniadakis entropy in [23,[26][27][28][29][30][31].…”

Section: Preliminariesmentioning

confidence: 99%

Discrete Entropies of Chebyshev Polynomials

Sfetcu,

Preda

2024

Mathematics

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Because of its flexibility and multiple meanings, the concept of information entropy in its continuous or discrete form has proven to be very relevant in numerous scientific branches. For example, it is used as a measure of disorder in thermodynamics, as a measure of uncertainty in statistical mechanics as well as in classical and quantum information science, as a measure of diversity in ecological structures and as a criterion for the classification of races and species in population dynamics. Orthogonal polynomials are a useful tool in solving and interpreting differential equations. Lately, this subject has been intensively studied in many areas. For example, in statistics, by using orthogonal polynomials to fit the desired model to the data, we are able to eliminate collinearity and to seek the same information as simple polynomials. In this paper, we consider the Tsallis, Kaniadakis and Varma entropies of Chebyshev polynomials of the first kind and obtain asymptotic expansions. In the particular case of quadratic entropies, there are given concrete computations.

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“…The reader can find other results and applications concerning the Kaniadakis entropy in [23,[26][27][28][29][30][31].…”

Section: Preliminariesmentioning

confidence: 99%

Discrete Entropies of Chebyshev Polynomials

Sfetcu,

Preda

2024

Mathematics

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“…Basit and Iqbal [16], Ebrahimi and Kirmani [11], Gupta and Nanda (2002), Abrham and Sankaran (2006), Nanda and Paul (2006) and Baig and Javid [17,18] gave the detailed overview on the residual entropy. Sunoj and Lino [15,19], Sunoj et al [20], Sati and Gupta [21], Thapliyal and Taneja [22], Thapliyal et al [23] produced their research on dynamic residual entropy, cumulative residual Tsallis entropy, Renyi entropy of order statistics and dynamic cumulative residual entropy. Ramdan [24], developed weighted entropy, weighted residual entropy and weighted pas entropy.…”

Section: Original Research Articlementioning

confidence: 99%

Some New Results of Residual and Past Entropy Measures

Basit

Iqbal

Lin

2021

AJPAS

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In this paper, two new generalized entropies have been introduced with their respective properties. The results of these entropies have been verified for the exponential and weighted exponential distributions. These two entropies produce the results in the form of simple entropy, generalized entropy, residual entropy, cumulative entropy and mixtures of all these entropies. Some characteristics of residual & past entropy have been derived and special cases have also been obtained. These cases indicate that new generalized entropies are more comprehensive and useful. The main advantage of this study is to derive different types of generalization of entropies using the different parameter values of α and β.

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“…The study of information measures based on QF is of recent interest. For some development in this direction, we refer to Baratpour and Khammar [1], Kayal [7], Sunoj et al [23], Khammar and Jahanshahi [10], Kayal and Tripathy [8], Sunoj, Sankaran and Nair [24], Sunoj, Krishnan and Sankaran [25], and the references therein.…”

Section: (11)mentioning

confidence: 99%

“…More recently, Sunoj et al [24] proposed a quantile-based cumulative Kullback-Leibler divergence and obtained some useful bounds and characterizations. Also, Sunoj et al [25] studied a quantile-based Tsallis entropy and its order statistics. However, Kayal and Tripathy [8] introduced Tsallis divergence of order α and proved some properties including bounds and effect of transformations.…”

Section: )mentioning

confidence: 99%

Quantile-Based Study of (Dynamic) Inaccuracy Measures

Kayal¹,

Moharana²,

Sunoj³

2019

Prob. Eng. Inf. Sci.

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In the present communication, we introduce quantile-based (dynamic) inaccuracy measures and study their properties. Such measures provide an alternative approach to evaluate inaccuracy contained in the assumed statistical models. There are several models for which quantile functions are available in tractable form, though their distribution functions are not available in explicit form. In such cases, the traditional distribution function approach fails to compute inaccuracy between two random variables. Various examples are provided for illustration purpose. Some bounds are obtained. Effect of monotone transformations and characterizations are provided.

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A quantile-based study of cumulative residual Tsallis entropy measures

Cited by 14 publications

References 22 publications

Discrete Entropies of Chebyshev Polynomials

Discrete Entropies of Chebyshev Polynomials

Some New Results of Residual and Past Entropy Measures

Quantile-Based Study of (Dynamic) Inaccuracy Measures

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