Some properties of cumulative Tsallis entropy of order 
                
                  
                
                $$\alpha $$
                
                  
                    α

Rajesh, G.; Sunoj, S. M.

doi:10.1007/s00362-016-0855-7

Cited by 48 publications

(12 citation statements)

References 13 publications

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“…Many other extensions of Shannon entropy are redefined by the idea in Rao et al (2004) via replacing f (x) by 1 − F(x); see, for example, the works done by Drissi et al (2008), Sunoj and Linu (2012), Psarrakos and Navarro (2013), Sati and Gupta (2015), Rajesh and Sunoj (2016) and Kundu et al (2016). Asadi and Zohrevand (2007) defined the dynamic version of the cumulative residual entropy (DCRE), which is the CRE of the residual random variable X t , and it is given by…”

Section: Introduction and Preliminary Resultsmentioning

confidence: 99%

Some Characterization Results on Dynamic Cumulative Past Inaccuracy Measure

Khorashadizadeh

2018

JIRSS

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Abstract. In this paper, borrowing the intuition in Rao et al. (2004), we introduce a cumulative version of the inaccuracy measure (CIM). Also we obtain interesting and applicable properties of CIM for different cases based on the residual, past and interval lifetime random variables. Relying on various applications of stochastic classes in reliability and information theory fields, we study new classes of the lifetime in terms of the CIM along with their relations with other famous aging classes. Furthermore, some characterization results are obtained under the proportional reversed hazard rate model. Finally, considering that the time t changes in the range (t 1 , t 2 ), an extension of the CIM, called the interval cumulative residual (past) inaccuracy (ICR(P)I), is derived. We investigate the ICRI's relation with its analogous version based on Shannon entropy.

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Section: Introduction and Preliminary Resultsmentioning

confidence: 99%

Some Characterization Results on Dynamic Cumulative Past Inaccuracy Measure

Khorashadizadeh

2018

JIRSS

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“…The cumulative residual Tsallis entropy (CRTE) was introduced in the literature [22], and the probability density function in Equation 11 was replaced by the survival function 𝐹 𝑥 𝑃 𝑋 𝑥 , with the following expressions:…”

Section: Cumulative Residual Tsallis Entropymentioning

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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“…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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Some properties of cumulative Tsallis entropy of order $$\alpha $$ α

Cited by 48 publications

References 13 publications

Some Characterization Results on Dynamic Cumulative Past Inaccuracy Measure

Some Characterization Results on Dynamic Cumulative Past Inaccuracy Measure

Image segmentation algorithm based on cumulative residual Tsallis entropy

Tsallis Entropy of a Used Reliability System at the System Level

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