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Stochastic Comparisons of Cumulative Entropies

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Stochastic Orders in Reliability and Risk

Part of the book series: Lecture Notes in Statistics ((LNSP,volume 208))

Abstract

The cumulative entropy is an information measure which is alternative to the differential entropy and is connected with a notion in reliability theory. Indeed, the cumulative entropy of a random lifetime X can be expressed as the expectation of its mean inactivity time evaluated at X. After a brief review of its main properties, in this paper, we relate the cumulative entropy to the cumulative inaccuracy and provide some inequalities based on suitable stochastic orderings. We also show a characterization property of the dynamic version of the cumulative entropy. In conclusion, a stochastic comparison between the empirical cumulative entropy and the empirical cumulative inaccuracy is investigated.

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Acknowledgements

This paper is dedicated to Moshe Shaked in admiration to his most profound contributions on stochastic orders. The corresponding author is grateful to Fabio Spizzichino for introducing Moshe Shaked to him in 1996, which started the collaboration behind the Di Crescenzo and Shaked [132] paper. Antonio Di Crescenzo and Maria Longobardi are partially supported by MIUR-PRIN 2008 “Mathematical models and computation methods for information processing and transmission in neuronal systems subject to stochastic dynamics”.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università di Salerno, Via Ponte don Melillo, I-84084, Fisciano, Italy

    Antonio Di Crescenzo

  2. Dipartimento di Matematica e Applicazioni, Università di Napoli Federico II, Via Cintia, I-80126, Napoli, Italy

    Maria Longobardi

Authors
  1. Antonio Di Crescenzo
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  2. Maria Longobardi
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Correspondence to Antonio Di Crescenzo .

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Editors and Affiliations

  1. Dept. Mathematics, Washington State University, Lighty 370, Pullman, 99164, Washington, USA

    Haijun Li

  2. Xiamen University, Xiamen, 361000, China, People's Republic

    Xiaohu Li

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Di Crescenzo, A., Longobardi, M. (2013). Stochastic Comparisons of Cumulative Entropies. In: Li, H., Li, X. (eds) Stochastic Orders in Reliability and Risk. Lecture Notes in Statistics(), vol 208. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6892-9_8

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