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. Moreover, parametric examples are provided for some of the results included in Pellerey and Navarro (2021) and in the present paper.