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Title: Testing for the generalized Poisson-inverse Gaussian distribution Authors:  Virtudes Alba-Fernandez - University of Jaen (Spain) [presenting]
Maria Dolores Jimenez-Gamero - Universidad de Sevilla (Spain)
Apostolos Batsidis - University of Ioannina (Greece)
Abstract: The generalized Poisson inverse Gaussian (GPIG) family is a flexible family of distributions, useful for modelling count data with different tail heaviness. It includes the Poisson, Poisson-inverse Gaussian and discrete stable distributions as special cases. A new goodness-of-fit test is proposed for the GPIP family which is based on the following: since the probability generating function (PGF) of the GPIP family is the unique PGF satisfying certain differential equation, and the empirical PGF, as well as its derivatives, consistently estimate the PGF, and its derivatives, the empirical PGF should approximately satisfy such an equation. The proposed test statistic is based on sizing the coefficients of the polynomials up in the cited empirical version of the equation. It is shown that the test is consistent against fixed alternatives. The null distribution of the test statistic can be consistently approximated by means of a parametric bootstrap and a weighted bootstrap. The finite sample performance of the proposed test is investigated by means of a simulation study, where the goodness of the proposed approximations is numerically studied and the test is compared, in terms of power, to others.