如何在 Python 中对多元对数正态分布进行采样？

Question

如何使用 Python 从多元对数正态分布中抽取数据？例如，对于多元正态分布，有两个选项。假设我们有一个 3 x 3 协方差矩阵和一个 3 维均值向量 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

我找到了 numpy 的 numpy.random.lognormal, but that only seems to work for univariate samples. I also noticed scipy's scipy.stats.lognorm。这似乎确实具有多变量样本的潜力。但是，我不知道该怎么做。

Answer 1

多变量对数正态分布随机变量 Rv 应该有这个属性: log(Rv) 应该服从正态分布。因此，问题实际上只是生成一个多元正态分布的随机变量 np.exp 它。

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]])

如何在 Python 中对多元对数正态分布进行采样？

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

python

statistics

numpy

probability

scipy