File:Generalized normal densities.svg

##
## Python code to generate density and CDF plots for the
## generalized normal distribution (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, b, mu):
    Y = np.abs(X-mu)/a
    Y = np.exp(-Y**b)
    Y = Y*b/(2*a)
    Y /= np.exp(sp.gammaln(1/float(b)))
    return Y
 
def cdf(X, a, b, mu):
    Y = dens(X, a, b, mu)
    Y = np.cumsum(Y)*(X[1]-X[0])
    return Y
 
w = 1.5
 
X = np.arange(-3, 3, 0.01)
 
plt.clf()
 
colors = ['aqua', 'black', 'lime', 'deeppink', 'darkorange', 'blue']
B = [0.5, 1, 1.5, 2, 3, 8]
 
F = []
for c,b in zip(colors, B):
    Y = dens(X, 1, b, 0)
    f = plt.plot(X, Y, '-', color=c, lw=w)
    F.append(f)
    plt.hold(True)
 
s = ["$\\beta=%s$" % str(b) for b in B]
 
b = plt.legend(tuple(F), tuple(s), 'upper left')
plt.ylabel("Density")
b.draw_frame(False)
 
plt.savefig("generalized_normal_densities.svg")
plt.savefig("generalized_normal_densities.png")
 
plt.clf()
 
F = []
for c,b in zip(colors, B):
    Y = cdf(X, 1, b, 0)
    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("generalized_normal_cdfs.svg")
plt.savefig("generalized_normal_cdfs.png")