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Statistical Hypothesis Testing with SAS and R by Dirk Taeger, Sonja Kuhnt

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Chapter 5

Poisson distribution

The Poisson distribution is often called the distribution of rare events for count data. In health sciences it is used to model survival or mortality data. Other applications include the number of traffic accidents and the number of machine failures over a specific time frame. The Poisson distribution is closely related to the binomial distribution (if the sample size c05-math-0001 is large and the success probability c05-math-0002 is small) and to the Gaussian distribution which is deployed in the statistical tests presented next.

5.1 Tests on the Poisson parameter

In this section we deal with the question, if the parameter c05-math-0003 of a Poisson distribution differs from a value c05-math-0004. The first test gives a solution to this hypothesis through a Gaussian approximation of the Poisson distribution, the second test shows how to perform an exact test. The third test deals with the question if the difference between two Poisson parameters differs from zero.

5.1.1 z-test on the Poisson parameter

Description: Tests if the parameter of a Poisson distribution differs from a specific value .
Assumptions: ...

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