File:Skew normal densities.svg

##
## Python code to generate this plot.
## Requires numpy, matplotlib, and the special functions module from 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 = ["$\\alpha=%s$" % str(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")