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Quantile-Based Probabilistic Mean Value Theorem for Distorted Distributions

An application of the quantile-based probabilistic mean value theorem to distorted random variables, working out the theorem for the proportional hazard rate model, the proportional reversed hazard rate model, and the 'new better than used' aging class, and connecting the results to quantile densities and the Lorenz curve.

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2501.00362

This paper applies the quantile-based probabilistic mean value theorem to distorted distributions, a family introduced in actuarial science. Building on a probabilistic version of the mean value theo…