Applications of the Quantile-Based Probabilistic Mean Value Theorem to Distorted Distributions
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.  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.
KeywordsQuantile function Distorted distribution Mean value theorem
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).