Multivariate Normal CDF in Python using scipy

After searching a lot, I think this blog entry by Noah H. Silbert describes the only readymade code from a standard library that can be used for computing the cdf for a multivariate normal in Python. Scipy has a way to do it but as mentioned in the blog, it is difficult to find. The approach is based on a paper by Alan Genz’s.

From the blog, this is how it works.

from scipy.stats import mvn
import numpy as np
low = np.array([-10, -10])
upp = np.array([.1, -.2])
mu = np.array([-.3, .17])
S = np.array([[1.2,.35],[.35,2.1]])
p,i = mvn.mvnun(low,upp,mu,S)
print p

0.2881578675080012

The scipy multivariate_normal from v1.1.0 has a cdf function built in now:

from scipy.stats import multivariate_normal as mvn
import numpy as np

mean = np.array([1,5])
covariance = np.array([[1, 0.3],[0.3, 1]])
dist = mvn(mean=mean, cov=covariance)
print("CDF:", dist.cdf(np.array([2,4])))

CDF: 0.14833820905742245

Documentation can be found here.