Stochastic dominance of a random variable by a convex combination of its independent copies has recently been shown to hold within the relatively narrow class of distributions with concave odds function. We show that a key property for this stochastic dominance result to hold is the subadditivity of the cumulative distribution function of the reciprocal of the random variable of interest, referred to as the inverted distribution. This enlarges significantly the family of distributions for which the dominance is verified. Moreover, we study the relation between the class of distributions with concave odds function and the class we introduce showing conditions under which the concavity of the odds function implies the subadditivity of inverted distribution