The normal centroid and powers of the pearson's X2 test and the kolmogorov-smirnov test
For the normal location family the noncentrality parameter of the non-central X2 distribution admits a simple closed form representation through the normal centroid. Exploiting this relation, we show how the normal centroid facilitates the evaluation of the powers of the Pearson's X2 test and the Kolmogorov-Smirnov test.