Stochastic Comparisons of Some Distances between Random Variables

Patricia Ortega-Jiménez, Miguel A. Sordo and Alfonso Suárez-Llorens
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Patricia Ortega-Jiménez: Departamento de Estadística e I. O., Facultad de Ciencias, Universidad de Cádiz, 11002 Cádiz, Spain
Miguel A. Sordo: Departamento de Estadística e I. O., Facultad de Ciencias, Universidad de Cádiz, 11002 Cádiz, Spain
Alfonso Suárez-Llorens: Departamento de Estadística e I. O., Facultad de Ciencias, Universidad de Cádiz, 11002 Cádiz, Spain

Mathematics, 2021, vol. 9, issue 9, 1-14

Abstract: 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.

Keywords: stochastic order; copula; distance; variability measure; premium principle (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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