from functools import partial

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


def my_kde_bandwidth(obj, fac=1./5):
    """We use Scott's Rule, multiplied by a constant factor."""
    return np.power(obj.n, -1./(obj.d+4)) * fac


loc1, scale1, size1 = (-2, 1, 175)
loc2, scale2, size2 = (2, 0.2, 50)
x2 = np.concatenate([np.random.normal(loc=loc1, scale=scale1, size=size1),
                     np.random.normal(loc=loc2, scale=scale2, size=size2)])

x_eval = np.linspace(x2.min() - 1, x2.max() + 1, 500)

kde = stats.gaussian_kde(x2)
kde2 = stats.gaussian_kde(x2, bw_method='silverman')
kde3 = stats.gaussian_kde(x2, bw_method=partial(my_kde_bandwidth, fac=0.2))
kde4 = stats.gaussian_kde(x2, bw_method=partial(my_kde_bandwidth, fac=0.5))

pdf = stats.norm.pdf
bimodal_pdf = pdf(x_eval, loc=loc1, scale=scale1) * float(size1) / x2.size + \
              pdf(x_eval, loc=loc2, scale=scale2) * float(size2) / x2.size

fig = plt.figure(figsize=(8, 6))
ax = fig.add_subplot(111)

ax.plot(x2, np.zeros(x2.shape), 'b+', ms=12)
ax.plot(x_eval, kde(x_eval), 'k-', label="Scott's Rule")
ax.plot(x_eval, kde2(x_eval), 'b-', label="Silverman's Rule")
ax.plot(x_eval, kde3(x_eval), 'g-', label="Scott * 0.2")
ax.plot(x_eval, kde4(x_eval), 'c-', label="Scott * 0.5")
ax.plot(x_eval, bimodal_pdf, 'r--', label="Actual PDF")

ax.set_xlim([x_eval.min(), x_eval.max()])
ax.legend(loc=2)
ax.set_xlabel('x')
ax.set_ylabel('Density')

plt.show()