Dia 24/01/2013 - 16h
TÃtulo: Over- and Under-Dispersion Models.
Palestrante: CÃlestin Clotaire Kokonendji (Laboratoire de MathÃmatiques de BesanÃon, Università de Franche-Comtà - UFR Sciences et Techniques, BesanÃon, France)
Abstract: In this talk, we discuss some statistical modelling for count data from parametric and non parametric models. Over- and under-dispersion models must to be more flexible for practical use and admit special properties such duality with respect to the Poisson distribution. Different constructions of count models will be revisited in particular the weightening operation will be pointed out for unification in the new direction of research of univariate count models.
Apoio: FAPESP
Dia 24/01/2013 - 17h
Titulo: Discrete Dispersion Models and their Tweedie Asymptotics
Palestrante: Bent JÃrgensen, University of Southern Denmark
Abstract: We introduce a class of two-parameter discrete dispersion models, obtained by combining convolution with a factorial tilting operation, similar to exponential dispersion models which combine convolution and exponential tilting. The equidispersed Poisson model has a special place in this approach, whereas several overdispersed discrete distributions, such as the Hermite, Neyman Type A, PÃlya-Aeppli, negative binomial and Poisson-inverse Gaussian, turn out to be discrete Tweedie factorial dispersion models with power v-functions, similar to ordinary Tweedie exponential dispersion models with power variance functions. Using the factorial cumulant generating function we introduce a dilation operator, generalizing binomial thinning, which may be viewed as a discrete analogue of scaling. The discrete Tweedie factorial dispersion models are closed under dilation, which in turn leads to a discrete Tweedie asymptotic framework where discrete Tweedie models appear as dilation limits. This unifies many discrete convergence results and includes some new Poisson and Hermite convergence results, similar to the law of large numbers and the central limit theorem, respectively. The dilation operator also leads to a duality transformation which in some cases transforms overdispersion into underdispersion and vice-versa. Many of these results have multivariate analogues, and in particular we introduce a class of multivariate Poisson-Tweedie mixtures with discrete Tweedie margins. We also introduce a multivariate notion of over- and underdispersion, and a multivariate zero-inflation index. This is joint work with CÃlestin Kokonendji.
Apoio: PrÃ-Reitoria de PG, USP