Overlapping probability of two normal distribution with scipy

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.

How do i calculate it with scipy in Python? Thanks

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

Where the code for this looks like,

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()

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).

Starting Python 3.8, the standard library provides the NormalDist object as part of the statistics module.

NormalDist can be used to compute the overlapping coefficient (OVL) between two normal distributions via the NormalDist.overlap(other) method which returns a value between 0.0 and 1.0 giving the overlapping area for two probability density functions:

from statistics import NormalDist

NormalDist(mu=2.5, sigma=1).overlap(NormalDist(mu=5.0, sigma=1))
# 0.2112995473337106