A New Class of Fractional Cumulative Residual Entropy - Some Theoretical Results

Abstract

In this paper, by differentiating the entropy’s generating function (i.e., h(t) = R SX̄F tX (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.

Keywords

• cumulative residual entropy (CRE)
• entropy’s generating function
• fractional calculus
• information measure
• RiemannLiouville/Caputo fractional integral/derivative
• Tsallis/Rényi entropy