Python scipy - specify custom discrete distribution

Question

I use various continuous distributions from scipy.stats (e.g. norm). So if I want to find P(Z < 0.5) I would do:

from scipy.stats import norm
norm(0, 1).cdf(0.5)  # Z~N(0,1)

Is there a tool (scipy.stats or statsmodels or else) that I can use to describe a discrete distribution and then calculate CDF/CMF etc on it? I can write the code myself but I was wondering if something exists, for example:

pdf(x) = 1/3 for x = 1,2,3; else 0

Then I can construct 2 vectors x=[1,2,3], p = [1/3, 1/3, 1/3] and input them into a library class which will then provide .cdf() etc?

Answer 1

I guess you are looking for scipy.stats.rv_discrete here. From the docs:

rv_discrete is a base class to construct specific distribution classes and instances for discrete random variables. It can also be used to construct an arbitrary distribution defined by a list of support points and corresponding probabilities.

Example from docs:

from scipy import stats
xk = np.arange(7)
pk = (0.1, 0.2, 0.3, 0.1, 0.1, 0.0, 0.2)
custm = stats.rv_discrete(name='custm', values=(xk, pk))

And your example:

In [1]: import numpy as np

In [2]: from scipy import stats

In [3]: custm = stats.rv_discrete(name='custm', values=((1, 2, 3), (1./3, 1./3, 1./3)))

In [4]: custm.cdf(2.5)
Out[4]: 0.66666666666666663