Stochastic Comparisons of Some Distances between Random Variables

Stochastic Comparisons of Some Distances between Random Variables

The aim of this paper is twofold. First, we show that the expectation of the absolute value of the difference between two copies, not necessarily independent, of a random variable is a measure of its variability in the sense of Bickel and Lehmann (1979). Moreover, if the two copies are negatively de...

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Bibliographic Details
Main Authors: Patricia Ortega-Jiménez, Miguel A. Sordo, Alfonso Suárez-Llorens
Format: Article
Language:English
Published: MDPI AG 2021-04-01
Series:Mathematics
Subjects:
stochastic order
copula
distance
variability measure
premium principle
Online Access:https://www.mdpi.com/2227-7390/9/9/981
Description
Summary:The aim of this paper is twofold. First, we show that the expectation of the absolute value of the difference between two copies, not necessarily independent, of a random variable is a measure of its variability in the sense of Bickel and Lehmann (1979). Moreover, if the two copies are negatively dependent through stochastic ordering, this measure is subadditive. The second purpose of this paper is to provide sufficient conditions for comparing several distances between pairs of random variables (with possibly different distribution functions) in terms of various stochastic orderings. Applications in actuarial and financial risk management are given.
ISSN:2227-7390

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