arXiv subjects
Publications and source records attributed to Francisco Novoa-Muñoz.
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.
The bivariate Poisson distribution is commonly used to model bivariate count data. In this paper we study a goodness-of-fit test for this distribution. We also provide a review of the existing tests for the bivariate Poisson distribution, and its multivariate extension. The proposed test is consistent against any fixed alternative. It is also able to detect local alternatives converging to the null at the rate $n^{-\frac{1}{2}}$. The bootstrap can be employed to consistently estimate the null distribution of the test statistic. Through a simulation study we investigated the goodness of the bootstrap approximation and the power for finite sample sizes.
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.