O processo de Poisson estendido e aplicações
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Data
2007-06-14Autor
Salasar, Luis Ernesto Bueno
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Abstract
In this dissertation we will study how extended Poisson process can be applied to
construct discrete probabilistic models. An Extended Poisson Process is a continuous
time stochastic process with the state space being the natural numbers, it is obtained
as a generalization of homogeneous Poisson process where transition rates depend on
the current state of the process. From its transition rates and Chapman-Kolmogorov
di¤erential equations, we can determine the probability distribution at any …xed time of
the process. Conversely, given any probability distribution on the natural numbers, it
is possible to determine uniquely a sequence of transition rates of an extended Poisson
process such that, for some instant, the unidimensional probability distribution coincides
with the provided probability distribution. Therefore, we can conclude that extended
Poisson process is as a very ‡exible framework on the analysis of discrete data, since it
generalizes all probabilistic discrete models.
We will present transition rates of extended Poisson process which generate Poisson,
Binomial and Negative Binomial distributions and determine maximum likelihood estima-
tors, con…dence intervals, and hypothesis tests for parameters of the proposed models. We
will also perform a bayesian analysis of such models with informative and noninformative
prioris, presenting posteriori summaries and comparing these results to those obtained
by means of classic inference.