Tsallis Entropy Properties of Order Statistics and Some Stochastic Comparisons

Baratpour, Simindokht; Khammar, Amir Hamzeh

doi:10.18869/acadpub.jsri.13.1.2

Cited by 13 publications

(7 citation statements)

References 20 publications

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“…Ebrahimi et al [18] studied the information features of ordered random variables using Shannon entropy and the Kullback-Leibler distance. Similarly, Abbasnejad and Arghami [19] and Baratpour and Khammar [20] obtained similar results for the Renyi and Tsallis entropy of ordered random variables, respectively. Despite these efforts, the Tsallis entropy of the past lifetime of ordered variables has not been considered in literature thus far.…”

Section: Introductionsupporting

confidence: 54%

Some New Results Involving Past Tsallis Entropy of Order Statistics

Shrahili,

Kayid

2023

Entropy

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This work focuses on exploring the properties of past Tsallis entropy as it applies to order statistics. The relationship between the past Tsallis entropy of an ordered variable in the context of any continuous probability law and the past Tsallis entropy of the ordered variable resulting from a uniform continuous probability law is worked out. For order statistics, this method offers important insights into the characteristics and behavior of the dynamic Tsallis entropy, which is associated with past events. In addition, we investigate how to find a bound for the new dynamic information measure related to the lifetime unit under various conditions and whether it is monotonic with respect to the time when the device is idle. By exploring these properties and also investigating the monotonic behavior of the new dynamic information measure, we contribute to a broader understanding of order statistics and related entropy quantities.

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Section: Introductionsupporting

confidence: 54%

Some New Results Involving Past Tsallis Entropy of Order Statistics

Shrahili,

Kayid

2023

Entropy

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“…Furthermore, the stochastic order is also has many applications in finance, risk theory, management science and biomathematics. For example, we refer the reader to scholarly researches such as [1,6,9,11,14,19,20]. In this section, we introduce the Tsallis varentropy of order α for the ith order statistic.…”

Section: Tsallis Varentropy Of Order α For Order Statisticsmentioning

confidence: 99%

A New Generalized Varentropy and Its Properties

Maadani

Borzadaran

Roknabadi

2020

UMJ

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The variance of Shannon information related to the random variable \(X\), which is called varentropy, is a measurement that indicates, how the information content of \(X\) is scattered around its entropy and explains its various applications in information theory, computer sciences, and statistics. In this paper, we introduce a new generalized varentropy based on the Tsallis entropy and also obtain some results and bounds for it. We compare the varentropy with the Tsallis varentropy. Moreover, we explain the Tsallis varentropy of the order statistics and analyse this concept in residual (past) lifetime distributions and then introduce two new classes of distributions by them.

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“…It is suitable to study the behavior of the uncertainty of the new system in terms of Tsallis entropy. For other applications and researchers concerned with measuring the uncertainty of reliability systems, we refer readers to [ 15 , 16 , 17 , 18 ] and the references therein. In contrast to the work of Alomani and Kayid [ 14 ], the aim of this work is to study some uncertainty properties of a coherent system consisting of n components and having the property that at time

all components of the system are alive.…”

Section: Introductionmentioning

confidence: 99%

Tsallis Entropy of a Used Reliability System at the System Level

Kayid

Alshehri

2023

Entropy

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Measuring the uncertainty of the lifetime of technical systems has become increasingly important in recent years. This criterion is useful to measure the predictability of a system over its lifetime. In this paper, we assume a coherent system consisting of n components and having a property where at time t, all components of the system are alive. We then apply the system signature to determine and use the Tsallis entropy of the remaining lifetime of a coherent system. It is a useful criterion for measuring the predictability of the lifetime of a system. Various results, such as bounds and order properties for the said entropy, are investigated. The results of this work can be used to compare the predictability of the remaining lifetime between two coherent systems with known signatures.

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Tsallis Entropy Properties of Order Statistics and Some Stochastic Comparisons

Cited by 13 publications

References 20 publications

Some New Results Involving Past Tsallis Entropy of Order Statistics

Some New Results Involving Past Tsallis Entropy of Order Statistics

A New Generalized Varentropy and Its Properties

Tsallis Entropy of a Used Reliability System at the System Level

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