Goodness-of-Fit Test for the Bivariate Hermite Distribution

Abstract

This paper studies the goodness of fit test for the bivariate Hermite distribution. Specifically, we propose and study a Cramér–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.

Keywords

• bivariate Hermite distribution
• goodness-of-fit
• empirical probability generating function
• bootstrap distribution estimator