Calculate overlap area of two functions

I need to calculate the area where two functions overlap. I use normal distributions in this particular simplified example, but I need a more general procedure that adapts to other functions too. See image below to get an idea of what I mean, where the red area is what I'm after: 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 Carlo` to obtain the integral. The problem with this method is that when I evaluate sampled points in either distribution with `ker_b(sample)` (or `ker_a(sample)`), I get values placed directly over the KDE line. Because of this, even clearly overlapped distributions which should return a common/overlapped area value very close to 1. return instead small values (the total area of either curve is 1. since they are probability density estimates). How could I fix this code to give the expected results? This is how I applied Zhenya's answer ``` # 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.) ```