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title: "Introduction - Poisson Process"
canonical: "https://modelassist.epixanalytics.com/space/EA/26575359/Introduction%20-%20Poisson%20Process"
format: markdown
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# Estimating a Poisson intensity <span style="color: #222222">λ</span> using classical statistics

  


In many problems involving a Poisson process, we need to determine a Poisson rate or intensity (e.g. expected number of car crashes in a year, or concentration of particles suspended in a liquid). To do so, you will have had some observations a in a certain amount of exposure t. For example:

  


<span style="color: #222222">*α*</span> <span style="color: #000000">= counted particles         t = amount of liquid looked at</span>

<span style="color: #222222">*α*</span> <span style="color: #000000">= car crashes                  t = amount of time in which crashes occurred</span>

<span style="color: #222222">*α*</span> <span style="color: #000000">= typing errors                t = amount of text reviewed</span>

  


  


<span style="color: #000000">This section describes three methods:</span>

  


[Poisson distribution method](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26575360)

<span style="color: #000000">The crudest method, not recommended, but explained so you know why to avoid it.</span>

  


[Normal approximation to the Poisson distribution method](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26575361/)

<span style="color: #000000">Commonly used. It offers some improvement over the Poisson distribution method, but still cannot be applied when</span> a <span style="color: #000000">= 0, and gives incorrect results at extremes.</span>

  


[Cumulative confidence construction](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26575362/)

The best method that works for all values of a and t. It is also [closely aligned](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26575423/) to Bayesian results.

  


  


  


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