Tests de bondad de ajuste para la distribuci\'on Poisson bivariante

TL;DR

This paper develops and studies consistent goodness-of-fit tests for the bivariate Poisson distribution using the empirical probability generating function and differential equations, extending univariate methods.

Contribution

It introduces new goodness-of-fit tests for the bivariate Poisson distribution based on the empirical probability generating function and differential equations, which are consistent.

Findings

Tests are consistent for the bivariate Poisson distribution.

Two types of tests are proposed: Cramer-von Mises and polynomial coefficient-based.

Extensions of univariate goodness-of-fit tests to the bivariate case.

Abstract

The objective of this text is to propose and study goodness-of-fit tests for DBP, which are consistent. Since the probability generating function (fgp) characterizes the distribution of a random vector and can be estimated consistently by the empirical probability generating function (fgpe), the tests we propose are functions of the fgpe. The first statistical test compares the fgpe of the data with an estimator of the fgp of the DPB. Then, we show that the fgp of the DPB is the only fgp that satisfies a certain system of partial differential equations, which leads us to propose two statistical tests based on the empirical analogy of this system, one of them Cramer-von Mises type and the other is based on the coefficients of the polynomials of the empirical version. The tests we propose can be seen as extensions to the bivariate case of some goodness of fit tests designed for the univariate case.