Quantile based Tsallis entropy in residual lifetime

Khammar, Amir Hamzeh; Jahanshahi, Seyed Mahdi Amir

doi:10.1016/j.physa.2017.11.030

Cited by 13 publications

(7 citation statements)

References 28 publications

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“…51,52 Shannon 53 first proposed the concept of information entropy to describe the uncertainty and has applied in a lots of fields. 54,55 However, as in typical physical problems, there are some examples where the Boltzmann-Shannon entropy is not suitable. 56,57 In 1988, Tsallis proposed a non-extensive entropy called Tsallis entropy.…”

Section: Further Discussionmentioning

confidence: 99%

The generalization negation of probability distribution and its application in target recognition based on sensor fusion

Gao

Deng

2019

International Journal of Distributed Sensor Networks

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Target recognition in uncertain environments is a hot issue. Fusion rules are used to combine the sensor reports from different sources. In this situation, obtaining more information to make correct decision is an essential issue. Probability distribution is one of the most used methods to represent uncertainty information. In addition, the negation of probability distribution provides a new view to represent the uncertainty information. In this article, the existing negation of probability distribution is extended with Tsallis entropy. The main reason is that different systems have different parameter q. Some numerical examples are used to demonstrate the efficiency of the proposed method. Besides, the article also discusses the application of negation in target recognition based on sensor fusion to further demonstrate the importance of negation.

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Section: Further Discussionmentioning

confidence: 99%

The generalization negation of probability distribution and its application in target recognition based on sensor fusion

Gao

Deng

2019

International Journal of Distributed Sensor Networks

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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%

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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“…The measure (1.3) gives the expected uncertainty contained in the conditional density about the predictability of an outcome of X until 100(1 − u)% point of distribution. For the usefulness of information measures based on qf, we refer to [1,8,16,23,30] and the references therein. Recently, the concept of quantile-based information measures is extended for order statistics.…”

Section: Introductionmentioning

confidence: 99%

On quantile-based dynamic survival extropy and its applications

KHAMMAR,

AMİR JAHANSHAHİ,

ZAREİ

2023

Hacettepe Journal of Mathematics and Statistics

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The cumulative residual extropy is a uncertainty measure, that parallels extropy, in a absolutely continuous cumulative distribution function. The dynamic version of this measure is known as dynamic survival extropy. In this paper, we introduce a quantile version of dynamic survival extropy and study its properties. This approach gives a quantile measure of uncertainty. Unlike the dynamic survival extropy, the quantile-based dynamic survival extropy determines the quantile density function uniquely through a simple relationship. We also extend the definition of quantile-based dynamic survival extropy into order statistics. Finally, an application of new quantile-based uncertainty measure as a risk measure for some random variables having no closed form cumulative distribution functions is derived.

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Quantile based Tsallis entropy in residual lifetime

Cited by 13 publications

References 28 publications

The generalization negation of probability distribution and its application in target recognition based on sensor fusion

The generalization negation of probability distribution and its application in target recognition based on sensor fusion

Quantile-Based Study of (Dynamic) Inaccuracy Measures

On quantile-based dynamic survival extropy and its applications

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