问题描述
使用Python，如何从多元对数正态分布中采样数据?例如，对于多元法线，有两个选择.假设我们有一个3 x 3协方差矩阵和一个3维平均向量mu.
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
我发现numpy的 numpy.random.lognormal ，但这似乎仅适用于单变量样本.我还注意到scipy的 scipy .stats.lognorm .这似乎有可能用于多变量样本.但是，我不知道该怎么做.
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.
推荐答案
多元对数正态分布随机变量Rv应该具有此属性:log(Rv)应该遵循正态分布.因此，问题实际上仅在于生成多元正态分布的随机变量并np.exp.
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 = np.array([[1.0, 0.2, 0.3,],
[0.2, 1.0, 0.3,],
[0.3, 0.3, 1.0]])
In [3]: mu = np.log([0.3, 0.4, 0.5])
In [4]: mvn = nr.multivariate_normal(mu, cov, size=5)
In [5]: mvn # This is multivariate normal
Out[5]:
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]])
In [6]: mvln = np.exp(mvn)
In [7]: mvln # This is multivariate log-normal
Out[7]:
array([[ 0.25459314, 0.26563744, 0.139361 ],
[ 0.11869562, 3.60190996, 1.9347927 ],
[ 0.05925514, 0.29375578, 0.72154754],
[ 0.60849968, 0.70843576, 0.12991938],
[ 0.42489961, 0.28045684, 0.49184289]])
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