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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.
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
Full Text: DOI
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