Intensity Estimation for Poisson Processes

Introduction

This web page contains supplementary material for the following project:

• Ludwik Drazek, Intensity Estimation for Poisson Processes.
  MSc thesis, University of Leeds, Department of Statistics, 2012/13.

Abstract

This work investigates the modelling of data by a non-homogeneous Poisson process. The mathematical theory behind the Poisson distribution is introduced, this leads to the homogeneous Poisson process. The non-homogeneous Poisson process is developed as a generalisation of the homogeneous case. The theory behind the estimation of the non-homogeneous intensity function is developed. Throughout, R is used as the statistical software to graphically and numerically described the data and as the programming language to estimate the intensity functions. Several classes of intensity functions are considered and the parameters are found by maximum likelihood estimation. The resulting models are found to fit the data fairly well.

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• final version of the project report

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