16,180 research outputs found
Twisted Poincare duality for some quadratic Poisson algebras
Get PDFWe exhibit a Poisson module restoring a twisted Poincaré duality between Poisson homology and cohomology for the polynomial algebra R=C[X1Xn] endowed with Poisson bracket arising from a uniparametrised quantum affine space. This Poisson module is obtained as the semiclassical limit of the dualising bimodule for Hochschild homology of the corresponding quantum affine space. As a corollary we compute the Poisson cohomology of R, and so retrieve a result obtained by direct methods (so completely different from ours) by Monnier
Consistency and asymptotic normality of the maximum likelihood estimator in a zero-inflated generalized Poisson regression
Get PDFPoisson regression models for count variables have been utilized in many applications. However, in many problems overdispersion and zero-inflation occur. We study in this paper regression models based on the generalized Poisson distribution (Consul (1989)). These regression models which have been used for about 15 years do not belong to the class of generalized linear models considered by (McCullagh and Nelder (1989)) for which an established asymptotic theory is available. Therefore we prove consistency and asymptotic normality of a solution to the maximum likelihood equations for zero-inflated generalized Poisson regression models. Further the accuracy of the asymptotic normality approximation is investigated through a simulation study. This allows to construct asymptotic confidence intervals and likelihood ratio tests
Lattice permutations and Poisson-Dirichlet distribution of cycle lengths
Get PDFWe study random spatial permutations on ℤ3 where each jump x↦π(x) is penalized by a factor e−T∥x−π(x)∥2 . The system is known to exhibit a phase transition for low enough T where macroscopic cycles appear. We observe that the lengths of such cycles are distributed according to Poisson-Dirichlet. This can be explained heuristically using a stochastic coagulation-fragmentation process for long cycles, which is supported by numerical data
Poisson and Hochschild cohomology and the semiclassical limit
Get PDFLet be a quantum algebra possessing a semiclassical limit . We show
that under certain hypotheses can be thought of as a deformation of the
Poisson enveloping algebra of , and we give a criterion for the Hochschild
cohomology of to be a deformation of the Poisson cohomology of in the
case that is Koszul. We verify that condition for the algebra of quantum matrices and calculate its Hochschild cohomology and the Poisson
cohomology of its semiclassical limit
Poisson algebras via model theory and differential-algebraic geometry
Get PDFBrown and Gordon asked whether the Poisson Dixmier–Moeglin equivalence holds for any complex affine Poisson algebra, that is, whether the sets of Poisson rational ideals, Poisson primitive ideals, and Poisson locally closed ideals coincide. In this article a complete answer is given to this question using techniques from differential-algebraic geometry and model theory. In particular, it is shown that while the sets of Poisson rational and Poisson primitive ideals do coincide, in every Krull dimension at least four there are complex affine Poisson algebras with Poisson rational ideals that are not Poisson locally closed. These counterexamples also give rise to counterexamples to the classical (noncommutative) Dixmier–Moeglin equivalence in finite GK dimension. A weaker version of the Poisson Dixmier–Moeglin equivalence is proven for all complex affine Poisson algebras, from which it follows that the full equivalence holds in Krull dimension three or less. Finally, it is shown that everything, except possibly that rationality implies primitivity, can be done over an arbitrary base field of characteristic zero
Complementarities and Macroeconomics: Poisson Games
Get PDFIn many situations in macroeconomics strategic complementarities arise, and agents face a coordination problem. An important issue, from both a theoretical and a policy perspective, is equilibrium uniqueness. We contribute to this literature by focusing on the macroeconomic aspect of the problem: the number of potential innovators, speculators e.t.c. is large. In particular, we follow Myerson (1998, 2000) that in large games “a more realistic model should admit some uncertainty about the number of players in the game”. In more detail, we model the coordination problem as a Poisson game, and investigate the conditions under which unique equilibrium selection is obtained.Strategic Complementarities, Coordination Games, Poisson Games, Currency Crises, Innovation.
A priori ratemaking using bivariate poisson regression models
Get PDFIn automobile insurance, it is useful to achieve a priori ratemaking by resorting to generalized linear models, and here the Poisson regression model constitutes the most widely accepted basis. However, insurance companies distinguish between claims with or without bodily injuries, or claims with full or partial liability of the insured driver. This paper examines an a priori ratemaking procedure when including two di®erent types of claim. When assuming independence between claim types, the premium can be obtained by summing the premiums for each type of guarantee and is dependent on the rating factors chosen. If the independence assumption is relaxed, then it is unclear as to how the tariff system might be affected. In order to answer this question, bivariate Poisson regression models, suitable for paired count data exhibiting correlation, are introduced. It is shown that the usual independence assumption is unrealistic here. These models are applied to an automobile insurance claims database containing 80,994 contracts belonging to a Spanish insurance company. Finally, the consequences for pure and loaded premiums when the independence assumption is relaxed by using a bivariate Poisson regression model are analysed.
Mixture of bivariate Poisson regression models with an application to insurance
Get PDFIn a recent paper Bermúdez [2009] used bivariate Poisson regression models for ratemaking in car insurance, and included zero-inflated models to account for the excess of zeros and the overdispersion in the data set. In the present paper, we revisit this model in order to consider alternatives. We propose a 2-finite mixture of bivariate Poisson regression models to demonstrate that the overdispersion in the data requires more structure if it is to be taken into account, and that a simple zero-inflated bivariate Poisson model does not suffice. At the same time, we show that a finite mixture of bivariate Poisson regression models embraces zero-inflated bivariate Poisson regression models as a special case. Additionally, we describe a model in which the mixing proportions are dependent on covariates when modelling the way in which each individual belongs to a separate cluster. Finally, an EM algorithm is provided in order to ensure the models’ ease-of-fit. These models are applied to the same automobile insurance claims data set as used in Bermúdez [2009] and it is shown that the modelling of the data set can be improved considerably.Zero-inflation, Overdispersion, EM algorithm, Automobile insurance, A priori ratemaking.
Bivariate Poisson and Diagonal Inflated Bivariate Poisson Regression Models in R
Get PDFIn this paper we present an R package called bivpois for maximum likelihood estimation of the parameters of bivariate and diagonal inflated bivariate Poisson regression models. An Expectation-Maximization (EM) algorithm is implemented. Inflated models allow for modelling both over-dispersion (or under-dispersion) and negative correlation and thus they are appropriate for a wide range of applications. Extensions of the algorithms for several other models are also discussed. Detailed guidance and implementation on simulated and real data sets using bivpois package is provided.
Simulating the tail of the interference in a Poisson network model
Get PDFInterference among simultaneous transmissions represents the main limitation factor for the capacity and connectivity of dense wireless networks. In this paper we provide efficient simulation laws for the tail of the interference in a simple wireless ad hoc network model. Particularly, we consider node locations distributed according to a Poisson point process and various classes of light-tailed fading distribution
- …
