Mack Mack - 7 months ago 65
Python Question

How can I sample a multivariate log-normal distribution in Python?

Using Python, how can I sample data from a multivariate log-normal distribution? For instance, for a multivariate normal, there are two options. Let's assume we have a 3 x 3 covariance matrix and a 3-dimensional mean vector mu.

# Method 1
sample = np.random.multivariate_normal(mu, covariance)

# Method 2
L = np.linalg.cholesky(covariance)
sample = L.dot(np.random.randn(3)) + mu


I found numpy's numpy.random.lognormal, but that only seems to work for univariate samples. I also noticed scipy's scipy.stats.lognorm. This does seem to have the potential for multivariate samples. However, I can't figure out how to do this.

Answer

A multivariate lognormal distributed random variable Rv should have this property: log(Rv) should follow a normal distribution. Therefore, the problem is really just to generation a random variable of multivariate normal distribution and np.exp it.

In [1]:

import numpy.random as nr
In [2]:

cov = [[1.0, 0.2, 0.3,],
       [0.2, 1.0, 0.3,],
       [0.3, 0.3, 1.0]]
cov = np.array(cov)
In [3]:

mu  = np.log([0.3, 0.4, 0.5])
In [4]:

rv = nr.multivariate_normal(mu, cov, size=5)
rv
Out[4]:
array([[-1.36808854, -1.32562291, -1.9706876 ],
       [-2.13119289,  1.28146425,  0.66000019],
       [-2.82590272, -1.22500654, -0.32635701],
       [-0.4967589 , -0.34469589, -2.04084115],
       [-0.85590235, -1.27133544, -0.70959595]])
#5 points in the resultant np.array

np.exp(rv) would be multivariate lognormal distributed.

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