skew normal distribution in scipy

Question

Does anyone know how to plot a skew normal distribution with scipy? I supose that stats.norm class can be used but I just can't figure out how. Furthermore, how can I estimate the parameters describing the skew normal distribution of a unidimensional dataset?

Solution 1

From the Wikipedia description,

from scipy import linspace
from scipy import pi,sqrt,exp
from scipy.special import erf

from pylab import plot,show

def pdf(x):
    return 1/sqrt(2*pi) * exp(-x**2/2)

def cdf(x):
    return (1 + erf(x/sqrt(2))) / 2

def skew(x,e=0,w=1,a=0):
    t = (x-e) / w
    return 2 / w * pdf(t) * cdf(a*t)
    # You can of course use the scipy.stats.norm versions
    # return 2 * norm.pdf(t) * norm.cdf(a*t)


n = 2**10

e = 1.0 # location
w = 2.0 # scale

x = linspace(-10,10,n) 

for a in range(-3,4):
    p = skew(x,e,w,a)
    plot(x,p)

show()

If you want to find the scale, location, and shape parameters from a dataset use scipy.optimize.leastsq, for example using e=1.0,w=2.0 and a=1.0,

fzz = skew(x,e,w,a) + norm.rvs(0,0.04,size=n) # fuzzy data

def optm(l,x):
    return skew(x,l[0],l[1],l[2]) - fzz

print leastsq(optm,[0.5,0.5,0.5],(x,))

should give you something like,

(array([ 1.05206154,  1.96929465,  0.94590444]), 1)

Solution 2

The accepted answer is more or less outdated, because a skewnorm function is now implemented in scipy. So the code can be written a lot shorter:

 from scipy.stats import skewnorm
 import numpy as np
 from matplotlib import pyplot as plt
 
 X = np.linspace(min(your_data), max(your_data))
 plt.plot(X, skewnorm.pdf(X, *skewnorm.fit(your_data)))