Solutions to the parameter estimation problem of the multivariate Pareto distribution of Asimit et al. (2010) are developed and exemplified numerically. Namely, a density of the aforementioned multivariate Pareto distribution with respect to a dominating measure, rather than the corresponding...

Starting from the question: “What is the accident risk of an insured?”, this paper considers a multivariate approach by taking into account three types of accident risks and the possible dependence between them. Driven by a real data set, we propose three trivariate Sarmanov distributions...

A multivariate probability model possessing a dependence structure that is reflected in its variance covariance structure and gamma distributed univariate margins is introduced and studied. In particular, the higher order moments and cumulants, Chebyshev’s type inequalities and multivariate...

Distorted expectations can be expressed as weighted averages of quantiles. In this note, we show that this statement is true, but that one has to be careful with the correct formulation of it. Furthermore, the proofs of the additivity property for distorted expectations of a comonotonic sum that...