Fitting aggregated counts to the Poisson distribution
The Poisson distribution is named after the French mathematician Poisson, who published a thesis about it in 1837. The Poisson distribution is a discrete distribution usually associated with counts for a fixed interval of time or space. It is only defined for integer values k. For instance, we could apply it to monthly counts of rainy days. In this case, we implicitly assume that the event of a rainy day occurs at a fixed monthly rate. The goal of fitting the data to the Poisson distribution is to find the fixed rate.
The following equations describe the probability mass function (3.5) and rate parameter (3.6) of the Poisson distribution:
How to do it...
The following steps fit using the maximum ...
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