Abstract
We consider the cumulative residual entropy (CRE) a recently introduced measure of entropy. While in previous works distributions with positive support are considered, we generalize the definition of CRE to the case of distributions with general support. We show that several interesting properties of the earlier CRE remain valid and supply further properties and insight to problems such as maximum CRE power moment problems. In addition, we show that this generalized CRE can be used as an alternative to differential entropy to derive information-based optimization criteria for system identification purpose.
Highlights
The concept of entropy is important for studies in many areas of engineering such as thermodynamics, mechanics, or digital communications
Considering the complementary cumulative distribution function (CCDF) instead of the probability density function in the definition of differential entropy leads to a new entropy measure named cumulative residual entropy (CRE) [3, 4]
We resort to mutual information (MI) to estimate a as the coefficient α such that random variable (RV) Ynα = Xn − αXn−1 and Yn show the highest dependence
Summary
The concept of entropy is important for studies in many areas of engineering such as thermodynamics, mechanics, or digital communications. Considering the complementary cumulative distribution function (CCDF) instead of the probability density function in the definition of differential entropy leads to a new entropy measure named cumulative residual entropy (CRE) [3, 4]. Following the work in [4], a modified version of the exponential entropy, where PDF is replaced by CCDF, has been introduced in [6], leading to new entropy-type measures, called survival entropies. Both Rao et al.’s CRE and its exponential entropy generalization by Zografos and Nadarajah lead to entropy-type definitions that assume either positive valued RVs or apply to |X| otherwise. Putting all pieces together one proves convergence of right-hand side of (2)
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