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Applications of the Quantile-Based Probabilistic Mean Value Theorem to Distorted Distributions

  • Antonio Di CrescenzoEmail author
  • Barbara Martinucci
  • Julio Mulero
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10672)

Abstract

Distorted distributions were introduced in the context of actuarial science for several variety of insurance problems. In this paper we consider the quantile-based probabilistic mean value theorem given in Di Crescenzo et al. [4] and provide some applications based on distorted random variables. Specifically, we consider the cases when the underlying random variables satisfy the proportional hazard rate model and the proportional reversed hazard rate model. A setting based on random variables having the ‘new better than used’ property is also analyzed.

Keywords

Quantile function Distorted distribution Mean value theorem 

Notes

Acknowledgements

The research of A. Di Crescenzo and B. Martinucci has been performed under partial support by the Group GNCS of INdAM. J. Mulero acknowledges support received from the Ministerio de Economía, Industria y Competitividad under grant MTM2016-79943-P (AEI/FEDER, UE).

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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Antonio Di Crescenzo
    • 1
    Email author
  • Barbara Martinucci
    • 1
  • Julio Mulero
    • 2
  1. 1.Dipartimento di MatematicaUniversità di SalernoFiscianoItaly
  2. 2.Departamento de MatemáticasUniversidad de AlicanteAlicanteSpain

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