Major in Mathematics!
A mathematics degree from New Paltz accommodates both applied and theoretical interests, and provides exceptional preparation for future careers in law, medicine, education, insurance, and business.
Our small class sizes enable students to work closely with faculty and receive the personal attention that only a liberal arts education can offer. Recent research projects have included angular determinations in pentagons; software development for algebraic evolution; and modeling the success of protest groups, to name a few.
With major tracks in mathematics, adolescence education in mathematics, and elementary education in mathematics, our graduates go on to attend Ph.D. programs, work as financial analysts on Wall Street, secure positions at high-level companies like Microsoft, and teach mathematics in both public schools and the country's most prestigious universities.
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Location: FOB S14
Time: 11 a.m. — Noon
Date: Wednesday, April 29, 2015
On flexibility of multivariate Tweedie distributions
Johann CueninUniversité de Franche-Comté, Labortatoire de Mathématiques de Besançon
Abstract: Univariate Tweedie distributions were introduced by M. C. K. Tweedie in 1984 and
include some well-known distributions such as Gaussian, inverse Gaussian, gamma, α-stable or
Poisson. These laws are very useful in many fields of applications as in ecology, actuarial sciences, quality control or physics. Thus several works were set about the construction of multivariate Tweedie, but all of them propose models only for direct applications.
After the first part dedicated to recall the framework of Tweedie distributions, we introduce
the multivariate Tweedie distributions in the second part. We show that they resume some
characteristics of the Gaussian vector, with both positive and negative correlations. We also specify how to compute these distributions and give some simulation results. In the third part, we establish another type of multivariate Tweedie called multiple stable Tweedie (MST) models. These models are made by a fixed univariate and positive support Tweedie variable and the remaining elements are univariate Tweedie with dispersions parameters equal to the observation of the fixed variable.
Starting from this construction, we give the variance and generalized variance functions of MST models and show that the latter is the product of powered components of the mean vector. Through the establishment of associated modified Lévy measure, we also propose an estimator of generalized variance, which is unbiased and has uniformly minimum variance.