Goodness-of-fit test for the bivariate Hermite distribution

TL;DR

This paper introduces a new goodness-of-fit test for the bivariate Hermite distribution using a Cramér-von Mises approach based on the empirical probability generation function, with bootstrap methods for finite samples.

Contribution

It proposes a novel goodness-of-fit test for the bivariate Hermite distribution utilizing empirical probability generation functions and bootstrap techniques.

Findings

Bootstrap provides consistent null distribution estimation.

Simulation confirms effectiveness for finite samples.

Test performs well in identifying distribution fit.

Abstract

This paper studies the goodness of fit test for the bivariate Hermite distribution. Specifically, we propose and study a Cram\'er-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.