两个正态分布与 scipy 的重叠概率

问题描述

我有两条 scipy.stats.norm(mean, std).pdf(0) 正态分布曲线，我试图找出两条曲线的差异(重叠).

i have two scipy.stats.norm(mean, std).pdf(0) normal distribution curve and i am trying to find out the differential (overlapping) of the two curves.

我如何用 Python 中的 scipy 计算它?谢谢

How do i calculate it with scipy in Python? Thanks

推荐答案

您可以使用@duhalme 建议的答案来获得相交，然后使用此点来定义积分限制的范围，

You can use the answer suggested by @duhalme to get the intersect and then use this point to define the range of integral limits,

这里的代码看起来像，

import numpy as np
import matplotlib.pyplot as plt
from scipy.stats import norm
norm.cdf(1.96)

def solve(m1,m2,std1,std2):
  a = 1/(2*std1**2) - 1/(2*std2**2)
  b = m2/(std2**2) - m1/(std1**2)
  c = m1**2 /(2*std1**2) - m2**2 / (2*std2**2) - np.log(std2/std1)
  return np.roots([a,b,c])

m1 = 2.5
std1 = 1.0
m2 = 5.0
std2 = 1.0

#Get point of intersect
result = solve(m1,m2,std1,std2)

#Get point on surface
x = np.linspace(-5,9,10000)
plot1=plt.plot(x,norm.pdf(x,m1,std1))
plot2=plt.plot(x,norm.pdf(x,m2,std2))
plot3=plt.plot(result,norm.pdf(result,m1,std1),'o')

#Plots integrated area
r = result[0]
olap = plt.fill_between(x[x>r], 0, norm.pdf(x[x>r],m1,std1),alpha=0.3)
olap = plt.fill_between(x[x<r], 0, norm.pdf(x[x<r],m2,std2),alpha=0.3)

# integrate
area = norm.cdf(r,m2,std2) + (1.-norm.cdf(r,m1,std1))
print("Area under curves ", area)

plt.show()

这里使用 cdf 来获得高斯的积分，尽管可以定义高斯的符号版本并使用 scipy.quad(或其他东西).或者，您可以使用像这样的蒙特卡罗方法 link(即生成随机数并拒绝任何超出您想要的范围).

The cdf is used to obtain the integral of the Gaussian here, although symbolic version of the Gaussian could be defined and scipy.quad employed (or something else). Alternatively, you could use a Monte Carlo method like this link (i.e. generate random numbers and reject any outside the range you want).

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