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Characterizations using past entropy measures. (English) Zbl 1325.94049
Summary: 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 defined for a non-negative random variable. In this paper we extend this definition to the case of a distributions with support in $$\mathbb{R}$$. 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.
##### MSC:
 94A17 Measures of information, entropy 62B10 Statistical aspects of information-theoretic topics 62E10 Characterization and structure theory of statistical distributions 62N05 Reliability and life testing
##### Keywords:
cumulative entropy; past entropy; characterizations
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##### References:
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