Cumulative Residual and Relative Cumulative Residual Fisher Information and Their Properties

Kharazmi, Omid

doi:10.1109/tit.2021.3073789

Cited by 22 publications

(28 citation statements)

References 19 publications

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“…The χ 2 ( Ḡ, F) divergence can also be defined in an analogous manner. For more details, see Kharazmi and Balakrishnan [13].…”

Section: Preliminariesmentioning

confidence: 99%

“…. , Fn , the Jensen-cumulative residual Fisher (JCRF) information measure was defined by Kharazmi and Balakrishnan [13] as…”

Section: Preliminariesmentioning

confidence: 99%

“…Let X denote a continuous random variable on the support X with survival function Fθ (x). The cumulative residual Fisher (CRF) information measure, introduced by Kharazmi and Balakrishnan [13], is then defined as…”

Section: Introductionmentioning

confidence: 99%

“…Hence, this information measure will naturally be robust to the presence of outliers. Kharazmi and Balakrishnan [13] have analogously defined the CRF information measure for the survival function ( F) as…”

Section: Introductionmentioning

confidence: 99%

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Cumulative Residual q-Fisher Information and Jensen-Cumulative Residual χ2 Divergence Measures

Kharazmi

Jamali

2022

Entropy

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In this work, we define cumulative residual q-Fisher (CRQF) information measures for the survival function (SF) of the underlying random variables as well as for the model parameter. We also propose q-hazard rate (QHR) function via q-logarithmic function as a new extension of hazard rate function. We show that CRQF information measure can be expressed in terms of the QHR function. We define further generalized cumulative residual χ2 divergence measures between two SFs. We then examine the cumulative residual q-Fisher information for two well-known mixture models, and the corresponding results reveal some interesting connections between the cumulative residual q-Fisher information and the generalized cumulative residual χ2 divergence measures. Further, we define Jensen-cumulative residual χ2 (JCR-χ2) measure and a parametric version of the Jensen-cumulative residual Fisher information measure and then discuss their properties and inter-connections. Finally, for illustrative purposes, we examine a real example of image processing and provide some numerical results in terms of the CRQF information measure.

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“…The χ 2 ( Ḡ, F) divergence can also be defined in an analogous manner. For more details, see Kharazmi and Balakrishnan [13].…”

Section: Preliminariesmentioning

confidence: 99%

“…. , Fn , the Jensen-cumulative residual Fisher (JCRF) information measure was defined by Kharazmi and Balakrishnan [13] as…”

Section: Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Cumulative Residual q-Fisher Information and Jensen-Cumulative Residual χ2 Divergence Measures

Kharazmi

Jamali

2022

Entropy

Self Cite

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“…This is because the FI is an expectation with respect to X , it equally weights all X values, including large values that may be outliers. The cumulative residual Fisher information (abbreviated as CF) was recently presented by Kharazmi and Balakrishnan [26], which is naturally robust to the presence of outliers. This modified measure is defined as…”

Section: Introductionmentioning

confidence: 99%

Sarmanov bivariate distribution: dependence structure—Fisher information in order statistics and their concomitants

et al. 2022

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The Sarmanov family of bivariate distributions is considered as the most flexible and efficient extended families of the traditional Farlie–Gumbel–Morgenstern family. The goal of this work is twofold. The first part focuses on revealing some novel aspects of the Sarmanov family’s dependency structure. In the second part, we study the Fisher information (FI) related to order statistics (OSs) and their concomitants about the shape-parameter of the Sarmanov family. The FI helps finding information contained in singly or multiply censored bivariate samples from the Sarmanov family. In addition, the FI about the mean and shape parameter of exponential and power distributions in concomitants of OSs is evaluated, respectively. Finally, the cumulative residual FI in the concomitants of OSs based on the Sarmanov family is derived.

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Jensen-discrete information generating function with an application to image processing

Kharazmi

Ozonur

2023

Soft Comput

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Cumulative Residual and Relative Cumulative Residual Fisher Information and Their Properties

Cited by 22 publications

References 19 publications

Cumulative Residual q-Fisher Information and Jensen-Cumulative Residual χ2 Divergence Measures

Cumulative Residual q-Fisher Information and Jensen-Cumulative Residual χ2 Divergence Measures

Sarmanov bivariate distribution: dependence structure—Fisher information in order statistics and their concomitants

Jensen-discrete information generating function with an application to image processing

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