A Minimizing Problem of Distances Between Random Variables with Proportional Reversed Hazard Rate Functions

Let X be a random variable with distribution function F and let F_X be the family of proportional reversed hazard rate distribution functions associated to F. Given the random vector (X, Y) with copula C and respective marginal distribution functions F and G ∈ F_X, we obtain sufficient conditions for the existence of G ∈ F_X that minimizes E|X − Y |.

English

Note on Efron’s Monotonicity Property Under Given Copula Structures

Given a multivariate random vector, Efron's marginal monotonicity (EMM) refers to the stochastic monotonicity of the variables given the value of their sum. Recently, based on the notion of total positivity of the joint density of the vector, Pellerey and Navarro (2021) obtained su cient conditions for EMM when the monotonicity is in terms of the likelihood ratio order. We provide in this paper new su cient conditions based on properties of the marginals and the copula.

English