从Python中的联合分布计算边际分布

Question

I have these two arrays/matrices which represent the joint distribution of 2 discrete random variables X and Y. I represented them in this format because I wanted to use the numpy.cov function and that seems to be the format cov requires.

https://docs.scipy.org/doc/numpy-1.15.0/reference/generated/numpy.cov.html

joint_distibution_X_Y = [

    [0.01, 0.02, 0.03, 0.04, 
     0.01, 0.02, 0.03, 0.04, 
     0.01, 0.02, 0.03, 0.04, 
     0.01, 0.02, 0.03, 0.04],

    [0.002, 0.002, 0.002, 0.002, 
     0.004, 0.004, 0.004, 0.004, 
     0.006, 0.006, 0.006, 0.006, 
     0.008, 0.008, 0.008, 0.008],

]

join_probability_X_Y = [
                0.01, 0.02, 0.04, 0.04, 
                0.03, 0.24, 0.15, 0.06,
                0.04, 0.10, 0.08, 0.08,
                0.02, 0.04, 0.03, 0.02
            ]

How do I calculate the marginal distribution of X (and also of Y) from the so given joint distribution of X and Y? I mean... is there any library method which I can call?

I want to get as a result eg something like:

 X_values = [0.002, 0.004, 0.006, 0.008]
 X_weights = [0.110, 0.480, 0.300, 0.110]  

I want to avoid coding the calculation of the marginal distribution myself.
I assume there's already some Python library method for that.
What is it and how can I call it given the data I have?

Answer 1

You could use margins :

import numpy as np
from scipy.stats.contingency import margins

join_probability_X_Y = np.array([
                [0.01, 0.02, 0.04, 0.04],
                [0.03, 0.24, 0.15, 0.06],
                [0.04, 0.10, 0.08, 0.08],
                [0.02, 0.04, 0.03, 0.02]
            ])


x, y = margins(join_probability_X_Y)

print(x.T)

Output

[[0.11 0.48 0.3  0.11]]