##
## Python code used to generate this plot.
## Requires matplotlib, numpy, and the special functions module of scipy.
##

import matplotlib.pyplot as plt
import numpy as np
import scipy.special as sp

def dens(X, a):
    Y = 2*np.exp(-X**2/2)/np.sqrt(2*np.pi)
    Y *= sp.ndtr(a*X)
    return Y

def cdf(X, a):
    Y = dens(X, a)
    Y = np.cumsum(Y)*(X[1]-X[0])
    return Y

w = 1.5

X = np.arange(-3, 3, 0.01)

plt.clf()

colors = ['aqua', 'lime', 'deeppink', 'darkorange', 'blue']
B = [-4, -1, 0, 1, 4]

F = []
for c,b in zip(colors, B):
    Y = dens(X, b)
    f = plt.plot(X, Y, '-', color=c, lw=w)
    F.append(f)
    plt.hold(True)

s = ["$\\alpha=%s$" % b for b in B]

b = plt.legend(tuple(F), tuple(s), 'upper left')
plt.ylabel("Density")
b.draw_frame(False)

plt.savefig("skew_normal_densities.svg")
plt.savefig("skew_normal_densities.png")

plt.clf()

F = []
for c,b in zip(colors, B):
    Y = cdf(X, b)
    f = plt.plot(X, Y, '-', color=c, lw=w)
    F.append(f)
    plt.hold(True)

b = plt.legend(tuple(F), tuple(s), 'upper left')
plt.ylabel("Cumulative probability")
b.draw_frame(False)
plt.ylim(0,1)

plt.savefig("skew_normal_cdfs.svg")
plt.savefig("skew_normal_cdfs.png")