You can use spline to fit the [blue curve – peak/2], and then find it’s roots:
import numpy as np
from scipy.interpolate import UnivariateSpline
def make_norm_dist(x, mean, sd):
return 1.0/(sd*np.sqrt(2*np.pi))*np.exp(-(x - mean)**2/(2*sd**2))
x = np.linspace(10, 110, 1000)
green = make_norm_dist(x, 50, 10)
pink = make_norm_dist(x, 60, 10)
blue = green + pink
# create a spline of x and blue-np.max(blue)/2
spline = UnivariateSpline(x, blue-np.max(blue)/2, s=0)
r1, r2 = spline.roots() # find the roots
import pylab as pl
pl.plot(x, blue)
pl.axvspan(r1, r2, facecolor="g", alpha=0.5)
pl.show()
Here is the result: