NDLI: Cumulative Residual q-Fisher Information and Jensen-Cumulative Residual $χ^{2}$ Divergence Measures

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Cumulative Residual q-Fisher Information and Jensen-Cumulative Residual $χ^{2}$ Divergence Measures

Content Provider	MDPI
Author	Kharazmi, Omid Balakrishnan, Narayanaswamy Jamali, Hassan
Copyright Year	2022
Description	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.
Starting Page	341
e-ISSN	10994300
DOI	10.3390/e24030341
Journal	Entropy
Issue Number	3
Volume Number	24
Language	English
Publisher	MDPI
Publisher Date	2022-02-27
Access Restriction	Open
Subject Keyword	Entropy Shannon Entropy Q-fisher Information Cumulative Residual Fisher Information Jensen Inequality Hazard Function Cumulative Residual Chi-square Divergence Q-hazard Rate Function
Content Type	Text
Resource Type	Article

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