Some new findings on the cumulative residual Tsallis entropy

Toomaj, Abdolsaeed; Atabay, Habibollah Agh

doi:10.1016/j.cam.2021.113669

Cited by 13 publications

(7 citation statements)

References 40 publications

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“…Accordingly, the residual Tsallis entropy is defined as

where

is the probability density function (PDF) of

is the survival function of X and

is the quantile function of

. Various properties, generalizations and applications of

are investigated by Asadi et al [ 4 ], Nanda and Paul [ 5 ], Zhang [ 6 ], Irshad et al [ 7 ], Rajesh and Sunoj [ 8 ], Toomaj and Agh Atabay [ 9 ], Mohamed et al [ 10 ], among others.…”

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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“…Accordingly, the residual Tsallis entropy is defined as

where

is the probability density function (PDF) of

is the survival function of X and

is the quantile function of

. Various properties, generalizations and applications of

are investigated by Asadi et al [ 4 ], Nanda and Paul [ 5 ], Zhang [ 6 ], Irshad et al [ 7 ], Rajesh and Sunoj [ 8 ], Toomaj and Agh Atabay [ 9 ], Mohamed et al [ 10 ], among others.…”

Section: Introductionmentioning

confidence: 99%

Tsallis Entropy of a Used Reliability System at the System Level

Kayid

Alshehri

2023

Entropy

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“…However, the results obtained from image segmentation based on cumulative residual entropy are better when applied to specific images, while the segmentation details are poor. Toomaj et al [20] presented the cumulative residual Tsallis entropy in 2021, which is generated by including a generalized measure into the cumulative residual entropy. Mohamed [21] et al revealed some new properties of cumulative residual Tsallis entropy and applied this entropy measure to test the uniformity.…”

Section: Introductionmentioning

confidence: 99%

Image segmentation algorithm based on cumulative residual Tsallis entropy

Tian

Liu

Fan

2023

International Conference on Image, Signal Processing, and Pattern Recognition (ISPP 2023)

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An algorithm which applies Cumulative Residual Tsallis Entropy (CRTE) to threshold image segmentation is proposed. Cumulative residual Tsallis entropy is an uncertainty measure generalized from Shannon entropy. The approach utilizes the cumulative residual Tsallis entropy function as the objective function, specifies the threshold segmentation criterion, and finds the optimal cumulative residual Tsallis entropy function solution. This method is applied to Berkeley Segmentation Dataset and compared with several classical segmentation methods on the same dataset. Experiment findings suggest that this algorithm is capable of producing improved segmentation results.

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“…The literature teems with several results of the Shannon entropy and its related measures. Interested readers may refer to [14][15][16][17][18] for the Shannon entropy, Kullback-Leibler divergence, and Fisher information number; [19,20] for fractional cumulative residual entropy and cumulative residual entropy, respectively; [13,[21][22][23][24] for the Tsallis entropy and its related measures; and finally [25,26] for the extropy and Rényi entropy and its applications, respectively.…”

Section: Introductionmentioning

confidence: 99%

Cumulative Residual Tsallis Entropy-Based Test of Uniformity and Some New Findings

et al. 2022

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The Tsallis entropy is an extension of the Shannon entropy and is used extensively in physics. The cumulative residual Tsallis entropy, which is a generalization of the Tsallis entropy, plays an important role in the measurement uncertainty of random variables and has simple relationships with other important information and reliability measures. In this paper, some novel properties of the cumulative residual Tsallis entropy are disclosed. Moreover, this entropy measure is applied to testing the uniformity, where the limit distribution and an approximation of the distribution of the test statistic are derived. In addition, the property of stability is discussed. Furthermore, the percentage points and power against seven alternative distributions of this test statistic are presented. Finally, to compare the power of the suggested test with that of other tests of uniformity, a simulation study is conducted.

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Some new findings on the cumulative residual Tsallis entropy

Cited by 13 publications

References 40 publications

Tsallis Entropy of a Used Reliability System at the System Level

Tsallis Entropy of a Used Reliability System at the System Level

Image segmentation algorithm based on cumulative residual Tsallis entropy

Cumulative Residual Tsallis Entropy-Based Test of Uniformity and Some New Findings

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