1. Characterizations based on generalized cumulative residual entropy functions
- Author
-
Jorge Navarro and Georgios Psarrakos
- Subjects
Statistics and Probability ,Principle of maximum entropy ,Maximum entropy thermodynamics ,020206 networking & telecommunications ,02 engineering and technology ,01 natural sciences ,Joint entropy ,Entropy power inequality ,Differential entropy ,010104 statistics & probability ,Maximum entropy probability distribution ,Statistics ,0202 electrical engineering, electronic engineering, information engineering ,Applied mathematics ,0101 mathematics ,Random variable ,Entropy rate ,Mathematics - Abstract
The Shannon entropy and the cumulative residual entropy (CRE) of a random variable are useful tools in probability theory. Recently, a new concept called generalized cumulative residual entropy (GCRE) of order n was introduced and studied. It is related with the record values of a sequence of i.i.d. random variables and with the relevation transform. In this paper, we show that, under some assumptions, the GCRE function of a fixed order n uniquely determines the distribution function. Some characterizations of particular probability models are obtained from this general result.
- Published
- 2016