Supposing this procedure valid and running the risk to be wrong I´ll try the following interpretation. Suppose that we are dealing with a Neyman-Pearson N-P scheme: _______H0: Data is Gumbel (0, 1) against Ha: N(0, 1) By construction because the chosen bound is simultaneously the Gumbel skewness 5% quantile and the 95% one of the N(0,1) skewness data, alpha=5%, is the chance to reject a true Null, when I observe a test value smaller than the bound. Symmetrically when Ha is true and I get a test value larger than the bound, 5% probability, I reject the Alternative making a Type II error (beta). I ask, is this true, am I dealing, really, with an N-P test where the Power is 1- beta = 95%? Feedback truly welcomed. . .