Goodness-of-fit test for the bivariate Hermite distribution

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