Stochastic Comparisons of Some Distances between Random Variables

Mathematics

Alfonso Suárez-Llorens¹  Patricia Ortega-Jiménez¹  MiguelA. Sordo¹ 

[1] Departamento de Estadística e I. O., Facultad de Ciencias, Universidad de Cádiz, 11002 Cádiz, Spain;

关键词: stochastic order;    copula;    distance;    variability measure;    premium principle;   

DOI  :  10.3390/math9090981

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown