Python: finding the intersection point of two gaussian curves

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You want to find the x’s such that both gaussian functions have the same height.(i.e intersect)

You can do so by equating two gaussian functions and solve for x. In the end you will get a quadratic equation with coefficients relating to the gaussian means and variances. Here is the final result:

import numpy as np

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

result = solve(m1,m2,std1,std2)

The output is :

array([ 3.75])

You can plot the found intersections:

x = np.linspace(-5,9,10000)
plot1=plt.plot(x,mlab.normpdf(x,m1,std1))
plot2=plt.plot(x,mlab.normpdf(x,m2,std2))
plot3=plt.plot(result,mlab.normpdf(result,m1,std1),'o')

The plot will be:
enter image description here

If your gaussians have multiple intersections, the code will also find all of them(say m1=2.5, std1=3.0, m2=5.0, std2=1.0):
enter image description here

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