Fractional cumulative residual entropy.

• We generate the CRE to fractional order, named fractional CRE. • Some properties of the fractional CRE are presented. • The validity of fractional CRE is supported by numerical simulation and practical application. • The fractional CRE has inherited the merits of both CRE and fractional entropy. Recently, cumulative residual entropy was proposed as an alternative measure of information to Shannon entropy. In this work, we generate the cumulative residual entropy (CRE) to the case of fractional order, named fractional CRE. Some properties of the new quantity are presented. The connections of fractional CRE to the CRE and classic differential entropy are studied. Besides, we show that the proposed information measure can be estimated by the empirical fractional CRE of sample data. A central limit theorem for the empirical fractional CRE for random samples from the exponential distribution is derived. Its property of stability is also discussed. Finally, simulations on logistic map and application in financial data are given to support the validity of fractional CRE. [ABSTRACT FROM AUTHOR]