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Entropy-based measure of uncertainty in past lifetime distributions

  • Antonio Di Crescenzo (a1) and Maria Longobardi (a2)

As proposed by Ebrahimi, uncertainty in the residual lifetime distribution can be measured by means of the Shannon entropy. In this paper, we analyse a dual characterization of life distributions that is based on entropy applied to the past lifetime. Various aspects of this measure of uncertainty are considered, including its connection with the residual entropy, the relation between its increasing nature and the DRFR property, and the effect of monotonic transformations on it.

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Current address: Dipartimento di Matematica e Informatica, Università di Salerno, Via S. Allende, 84081 Baronissi (SA), Italy. Email address:
∗∗ Postal address: Dipartimento di Matematica e Applicazioni, Università di Napoli Federico II, Via Cintia, 80126 Napoli, Italy.
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Journal of Applied Probability
  • ISSN: 0021-9002
  • EISSN: 1475-6072
  • URL: /core/journals/journal-of-applied-probability
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