Characterizations using past entropy measures

摘要

It is reasonable to presume that in many realistic situations uncertainty is not necessarily related to the future but can also refer to the past. A measure of uncertainty in this context is the cumulative entropy denned for a non-negative random variable. In this paper we extend this definition to the case of a distributions with support in R. Conditions for the existence of this measure and its properties are also considered. Apart from this, certain characterization results based on past entropy measures are also discussed.