Python package that supports weighted covariance computation

Since version 1.10 numpy.cov does support weighted covariance compuation with the 'aweights' argument.

statsmodels has weighted covariance calculation in stats.

But we can still calculate it also directly:

# -*- coding: utf-8 -*-
"""descriptive statistic with case weights

Author: Josef Perktold
"""

import numpy as np
from statsmodels.stats.weightstats import DescrStatsW


np.random.seed(987467)
x = np.random.multivariate_normal([0, 1.], [[1., 0.5], [0.5, 1]], size=20)
weights = np.random.randint(1, 4, size=20)

xlong = np.repeat(x, weights, axis=0)

ds = DescrStatsW(x, weights=weights)

print 'cov statsmodels'
print ds.cov

self = ds  #alias to use copied expression
ds_cov = np.dot(self.weights * self.demeaned.T, self.demeaned) / self.sum_weights

print '\nddof=0'
print ds_cov
print np.cov(xlong.T, bias=1)

# calculating it directly
ds_cov0 = np.dot(self.weights * self.demeaned.T, self.demeaned) / \
              (self.sum_weights - 1)
print '\nddof=1'
print ds_cov0
print np.cov(xlong.T, bias=0)

This prints:

cov  statsmodels
[[ 0.43671986  0.06551506]
 [ 0.06551506  0.66281218]]

ddof=0
[[ 0.43671986  0.06551506]
 [ 0.06551506  0.66281218]]
[[ 0.43671986  0.06551506]
 [ 0.06551506  0.66281218]]

ddof=1
[[ 0.44821249  0.06723914]
 [ 0.06723914  0.68025461]]
[[ 0.44821249  0.06723914]
 [ 0.06723914  0.68025461]]

editorial note

The initial answer pointed out a bug in statsmodels that has been fixed in the meantime.