Chapter 4

# Poisson Regression

## 4.1 Introduction

Here Poisson regression is introduced and its connection to Cox regression is discussed. We start by defining the Poisson distribution, then discuss the connection to Cox regression and tabular lifetime data.

## 4.2 The Poisson Distribution

The Poisson distribution is used for count data, that is, when the result may be any positive integer 0, 1, 2,..., without upper limit. The probability density function (pdf) P of a random variable X following a Poisson distribution is

$\begin{array}{ll}\begin{array}{ll}P\left(X=k\right)=\frac{{\lambda}^{k}}{k!}\mathrm{exp}\left(-\lambda \right),\hfill & \lambda >0;\text{}\text{}k=0,1,2,\hfill \end{array}...,\hfill & (4.1)\hfill \end{array}$

The parameter λ is both the mean and the variance of the distribution. In Figure 4.1 the pdf (4.1) is plotted for some values of λ. Note that when λ increases, the distribution looks more and ...

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