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Characterizations using past entropy measures

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Abstract

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.

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Acknowledgments

We are thankful to Prof. Asok Nanda, IISER, Kolkata, India, for the fruitful discussion during the preparation of the manuscript. We are also thankful to the Associate Editor for his constructive suggestions apart from finding a mistake in Theorem (2.1) in the prerevised version and the anonymous referee for his remarks, both which substantially improved the paper.

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Authors and Affiliations

  1. Department of Statistics, Cochin University of Science and Technology, Cochin, 682022, Kerala, India

    G. Asha & C. J. Rejeesh

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  1. G. Asha
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  2. C. J. Rejeesh
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Correspondence to G. Asha.

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Asha, G., Rejeesh, C.J. Characterizations using past entropy measures. METRON 73, 119–134 (2015). https://doi.org/10.1007/s40300-014-0053-0

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  • DOI: https://doi.org/10.1007/s40300-014-0053-0

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