A New Class of Fractional Cumulative Residual Entropy - Some Theoretical Results
DOI:
https://doi.org/10.26636/jtit.2023.166622Keywords:
cumulative residual entropy (CRE), entropy’s generating function, fractional calculus, information measure, RiemannLiouville/Caputo fractional integral/derivative, Tsallis/Rényi entropyAbstract
In this paper, by differentiating the entropy’s generating function (i.e., h(t) = intsx Ft X (x) dx) using a Caputo fractional-order derivative, we derive a generalized non-logarithmic fractional cumulative residual entropy (FCRE). When the order of differentiation α → 1, the ordinary Rao CRE is recovered, which corresponds to the results from first-order ordinary differentiation. Some properties and examples of the proposed FCRE are also presented.
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