Functional Data Analysis for non homogeneous Poisson Processes

In this paper we intend to illustrate how functional data analysis (FDA) can be very useful for simulation input modelling. In particular, we are interested in the estimation of the cumulative mean function of a non-homogeneous Poisson process (NHPP). Both parametric and nonparametric methods have been developed to estimate it from observed independent streams of arrival times. As far as we know, these data have not been analyzed as functional data. The basic idea underlying of FDA is treating a functional observation as a single datum rather than as a large set of data on its own. A considerable effort is being made in order to adapt some standard statistical methods for functional data, for instance principal components analysis, ANOVA, classification techniques, bootstrap confidence bands, or outlier detection. We have studied a set of real data making use of these techniques and obtaining very good results.