We consider the problem of claims reserving and estimating run-off triangles. We generalize the gamma cell distributions model which leads to Tweedie’s compound Poisson model. Choosing a suitable parametrization, we estimate the parameters of our model within the framework of generalized linear models (see Jørgensen-de Souza [2] and Smyth-Jørgensen [8]). We show that these methods lead to reaso...

The aim of the paper is to extend the model of ”fishing problem”. The simple formulation is following. The angler goes to fishing. He buys fishing ticket for a fixed time. There are two places for fishing at the lake. The fishes are caught according to renewal processes which are different at both places. The fishes’ weights and the inter-arrival times are given by the sequences of i.i.d. rando...

We consider a bivariate Poisson model that is based on the lognormal heterogeneity model. Two recent applications have used this model. We suggest that the correlation estimated in their model frameworks is an ambiguous measure of the correlation of the variables of interest, and may substantially overstate it. We conclude with a detailed application of the proposed method using the data employ...

Simulating samples from arbitrary probability distributions is a major research program of statistical computing. Recent work has shown promise in an old idea, that sampling from a discrete distribution can be accomplished by perturbing and maximizing its mass function. Yet, it has not been clearly explained how this research project relates to more traditional ideas in the Monte Carlo literatu...

Abstract Weak solutions of a Vlasov-Schrödinger-Poisson system are shown to exist in the stationary and time-dependent situations. This system models the transport and interaction of electrons in a bidimensional electron gas. The particles are assumed to have a wave behaviour in the confinement directions (z) and to behave like point particles in the directions parallel to the electron gas (x)....

The objectives of this study are to: (1) examine the applicability of the double Poisson (DP) generalized linear model (GLM) for analyzing motor vehicle crash data characterized by over- and under-dispersion and (2) compare the performance of the DP GLM with the Conway-Maxwell-Poisson (COM-Poisson) GLM in terms of goodness-of-fit and theoretical soundness. The DP distribution has seldom been in...

The notion of a random graph was first introduced in 1947 by Erdös [27] to show the existence of a graph with a certain Ramsey property. A decade later, the theory of the random graph began with the paper entitled “On Random Graphs I” by Erdös and R、 enyi [28], and the theory had been developed by a series [29, 30, 31, 32, 33] of their papers. Since then, the subject has become one of the most ...

Excess zeros and overdispersion are commonly encountered phenomena that limit the use of traditional Poisson regression models for modeling count data. The focus of this paper is on modeling count data in the case that a population has excess zero counts and also consists of several sub-populations in the non-zero counts. The proposed zero-inflated Poisson regression mixture model accounts for ...

We continue the study of the Poisson-Sigma model over Poisson-Lie groups. Firstly, we solve the models with targets G and G∗ (the dual group of the Poisson-Lie group G) corresponding to a triangular r-matrix and show that the model over G∗ is always equivalent to BF-theory. Then, given an arbitrary r-matrix, we address the problem of finding D-branes preserving the duality between the models. W...