On the compounded bivariate Poisson distribution: A unified treatment

Abstract

Bivariate Poisson distribution, probability generating function, bivariate-Hermite, -negative binomial, -Poisson-Inverse Gaussian, -Neyman Type A, conditional distributions,

CMPH: a multivariate phase-type aggregate loss distribution

“…This shows that Case 1 is closely related to some results already reported in the literature, and next are two notes to illustrate the point. First, the pgf in equation (12) is that of the bivariate negative binomial distribution de ned in equation (3.9) of Kocherlakota [19] with parameter α = . We note in this regard that Kocherlakota [19] obtained the bivariate negative binomial distribution by mixing.…”

“…First, the pgf in equation (12) is that of the bivariate negative binomial distribution de ned in equation (3.9) of Kocherlakota [19] with parameter α = . We note in this regard that Kocherlakota [19] obtained the bivariate negative binomial distribution by mixing. Namely, assume that Ξ follows the exponential distribution with rate β.…”

“…It should be noted that relationships (19) do not hold when the claim sizes are not uniformly one, or when both types of claims may occur in a single claim combination (common shock). In such situations, capital allocations can be calculated with the help of the method noted earlier in Remark 7.…”

Transfer of Global Measures of Dependence into Cumulative Local

“…X Y As an illustration of this suggestion we consider the simplest Bivariate Poisson distribution constructed in the following way, borrowed from [9]. There are three Poisson distributed r.v.…”

Um Modelo Garma Bivariado Com Distribuição Condicional De Poisson

“…Já a literatura que aborda modelos de séries temporais multivariadas para dados de contagemé menos desenvolvida. A partir da dé-cada de 90, com o desenvolvimento de recursos computacionais, surgiram os primeiros modelos de regressão Poisson Bivariado com Jung e Winkelmann (1993), Kocherlakota e Kocherlakota (2001), Ho e Singer (2001), Karlis e Ntzoufras (2003,2005 dentre outros. No contexto de modelos estatísticos para séries temporais com dados de contagem, pode-se citar Davis (1999 Para uma melhor compreensão do modelo, dado uma análise de séries temporais de acidentes de carro, pode-se assumir que mesmo se o comportamento dos acidentes variar entre o dia e a noite, ambos os tipos de acidentes devem compartilhar alguns perigos comuns, como por exemplo, condições climáticas, a qualidade da estrada e "erro humano", istoé, a percepção e atenção falível.…”