Goodness-of-fit tests based on the empirical Wasserstein distance are proposed for simple and composite null hypotheses involving general multivariate distributions. For group families, procedure is to be implemented after preliminary reduction of data via invariance. This property allows calculation exact critical values p-values at finite sample sizes. Applications include testing location–sc...

This paper studies the goodness of fit test for bivariate Hermite distribution. Specifically, we propose and study a Cramér–von Mises-type based on empirical probability generation function. The bootstrap can be used to consistently estimate null distribution statistics. A simulation investigates approach finite sample sizes.