| Summary: | In this work, we define cumulative residual <i>q</i>-Fisher (CRQF) information measures for the survival function (SF) of the underlying random variables as well as for the model parameter. We also propose <i>q</i>-hazard rate (QHR) function via <i>q</i>-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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>χ</mi><mn>2</mn></msup></semantics></math></inline-formula> divergence measures between two SFs. We then examine the cumulative residual <i>q</i>-Fisher information for two well-known mixture models, and the corresponding results reveal some interesting connections between the cumulative residual <i>q</i>-Fisher information and the generalized cumulative residual <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>χ</mi><mn>2</mn></msup></semantics></math></inline-formula> divergence measures. Further, we define Jensen-cumulative residual <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>χ</mi><mn>2</mn></msup></semantics></math></inline-formula> (JCR-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>χ</mi><mn>2</mn></msup></semantics></math></inline-formula>) 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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