Python Data Analysis Cookbook

Fitting aggregated data to the gamma distribution

The gamma distribution can be used to model the size of insurance claims, rainfall, and the distribution of inter-spike intervals in brains. The PDF for the gamma distribution is defined by shape k and scale θ as follows:

There is also a definition that uses an inverse scale parameter (used by SciPy). The mean and variance of the gamma distribution are described by (3.3) and (3.4). As you can see, we can estimate the shape parameter from the mean and variance using simple algebra.

How to do it...

Let's fit aggregates for the rain data for January to the gamma distribution:

1. Start with the following imports: ...