On the Asymptotic Power of the “Energy” Test for the Equality of Two Distributions

In this study, the asymptotic distribution and the formula for the asymptotic power are found for the “energy” test of the hypotheses on the equality of two distributions in the case of alternative distributions that differ from the zero distribution by the shift parameter and/or the scale parameter. This criterion is an alternative to the well-known Mann—Whitney U test and, as distinct from the latter, allows distributions that differ in terms of the scale parameter to be compared. The efficiency of the results obtained is demonstrated by stochastic simulation for the normal and Cauchy distributions.