The Poisson process is one of the simplest stochastic processes and that is why it is often considered as the first mathematical model in many applications. There is a large amount of literature on the applications of Poisson process models in different domains (astronomy, biology, image analysis, medicine, optical communication, physics, reliability theory, etc.). At the same time, the identification of many important models of Poisson processes (as well as a general theory of estimation) has not yet been well developed, and such an attempt would help to cover this gap. We also note that the class of inhomogeneous Poisson processes is quite rich and is an interesting model for statistical investigation. The intensity functions may be sufficiently complicated to reflect, say, the real technical problems and therefore the estimation problems are not trivial.
KeywordsPoisson Process Intensity Function Asymptotic Normality Bayesian Estimator Regular Case
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