使用 scipy 在 Python 中实现多元正态 CDF [英] Multivariate Normal CDF in Python using scipy
问题描述
为了计算多元正态的 CDF,我遵循了这个示例(对于单变量情况)但无法解释 scipy 产生的输出:
In order to calculate the CDF of a multivariate normal, I followed this example (for the univariate case) but cannot interpret the output produced by scipy:
from scipy.stats import norm
import numpy as np
mean = np.array([1,5])
covariance = np.matrix([[1, 0.3 ],[0.3, 1]])
distribution = norm(loc=mean,scale = covariance)
print distribution.cdf(np.array([2,4]))
产生的输出是:
[[ 8.41344746e-01 4.29060333e-04]
[ 9.99570940e-01 1.58655254e-01]]
如果联合 CDF 定义为:
If the joint CDF is defined as:
P (X1 ≤ x1, . . . ,Xn ≤ xn)
那么预期输出应该是一个介于 0 和 1 之间的实数.
then the expected output should be a real number between 0 and 1.
推荐答案
找了很多,我觉得this 由 Noah H. Silbert 撰写的博客条目描述了标准库中唯一的现成代码,可用于计算 Python 中多元正态的 cdf.Scipy 有办法做到这一点,但正如博客中提到的那样,很难找到.该方法基于 Alan Genz 的一篇论文.
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.
来自博客,这是它的工作原理.
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
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