Statistical Properties of Estimators for The First and Second Order Derivatives of The Intensity Function of a Periodic Poisson Process.
Abstract
This manuscript is concerned with estimation of the first and second derivatives of intensity function of a periodic Poisson process. It is considered the worst condition if there is only available one realization of periodic Poisson process observed in interval [0, n ]. It is assumed that the period of this process is known. The main problem discussed in this manuscript is the formulation of asymptotic approximations to the bias and variance of the estimators for the first and second derivatives of the intensity of the process considered. In addition, computer simulations were carried out to study the behaviour of these asymptotic approximations for finite sample size.
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