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Calculate the overlap area of ​​two functions

I need to calculate the area where two functions overlap. I use regular distributions in this simplified example, but I need a more general procedure that also adapts to other functions.

See the image below to understand what I mean, where the red area is what I want:

enter image description here

This is the MWE I have so far:

import matplotlib.pyplot as plt
import numpy as np
from scipy import stats

# Generate random data uniformly distributed.
a = np.random.normal(1., 0.1, 1000)
b = np.random.normal(1., 0.1, 1000)

# Obtain KDE estimates foe each set of data.
xmin, xmax = -1., 2.
x_pts = np.mgrid[xmin:xmax:1000j]
# Kernels.
ker_a = stats.gaussian_kde(a)
ker_b = stats.gaussian_kde(b)
# KDEs for plotting.
kde_a = np.reshape(ker_a(x_pts).T, x_pts.shape)
kde_b = np.reshape(ker_b(x_pts).T, x_pts.shape)


# Random sample from a KDE distribution.
sample = ker_a.resample(size=1000)

# Compute the points below which to integrate.
iso = ker_b(sample)

# Filter the sample.
insample = ker_a(sample) < iso

# As per Monte Carlo, the integral is equivalent to the
# probability of drawing a point that gets through the
# filter.
integral = insample.sum() / float(insample.shape[0])

print integral

plt.xlim(0.4,1.9)
plt.plot(x_pts, kde_a)
plt.plot(x_pts, kde_b)

plt.show()

where I apply Monte Carloto get the integral.

, ker_b(sample) ( ker_a(sample)), , KDE. - , / , 1. ( 1., ).

, ?

# Calculate overlap between the two KDEs.
def y_pts(pt):
    y_pt = min(ker_a(pt), ker_b(pt))
    return y_pt
# Store overlap value.
overlap = quad(y_pts, -1., 2.)
+4
2

min(f(x), g(x)), f g - , . , scipy.integrate (quad , ), , , MC, ,

+5

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