Fitting a probability distribution to data with the maximum likelihood method

A good way to explain a dataset is to apply a probabilistic model to it. Finding an adequate model can be a job on its own. Once a model is chosen, it is necessary to compare it to the data. This is what statistical estimation is about. In this recipe, we apply the maximum likelihood method on a dataset of survival times after heart transplant (1967-1974 study).

Getting ready

As usual in this chapter, a background in probability theory and real analysis is recommended. In addition, you need the statsmodels package to retrieve the test dataset. It should be included in Anaconda, but you can always install it with the conda install statsmodels command.

How to do it...

1. statsmodels is a Python package for conducting statistical data analyses. It also contains real-world datasets that we can use when experimenting with new methods. Here, we load the heart dataset:

   >>> import numpy as np
       import scipy.stats as...