Kappa ratios and (higher-order) stochastic dominance

This paper first shows the sufficient relationship between the $$(n+1)$$ ( n + 1 ) -order SD and the n-order Kappa ratio. In fact, we clarify the restrictions on necessary beating of the target for the higher-order SD consistency of the Kappa ratios. Thereafter, we show that, in general, the necessary relationship between SD/RSD and the Kappa ratio cannot be established. We find that when the variables being compared belong to the same location-scale family or the same linear combination of location-scale families, we can get the necessary relationship between the $$(n+1)$$ ( n + 1 ) -order SD with the n-order Kappa ratio after imposing some conditions on the means. Our findings enable academics and practitioners to draw better decision in their analysis.