Some Properties of Fractional Cumulative Residual Entropy and Fractional Conditional Cumulative Residual Entropy

Abstract

Fractional cumulative residual entropy is a powerful tool for the analysis of complex systems. In this paper, we first provide some properties of fractional cumulative residual entropy (FCRE). Secondly, we generate cumulative residual entropy (CRE) to the case of conditional entropy, named fractional conditional cumulative residual entropy (FCCRE), and introduce some properties. Then, we verify the validity of these properties with randomly generated sequences that follow different distributions. Moreover, we give the definition of empirical fractional conditional accumulative residual entropy and prove that it can be used to approximate FCCRE. Finally, the empirical analysis of the aero-engine gas path data is carried out. The results show that FCRE and FCCRE can effectively capture complex information in the gas path system.