# -*- coding: utf-8 -*-
"""
Created on Mon Feb 09 15:13:03 2015

Listing 14.1 : densité de probabilité pour le chi-deux

@author: grivet
"""
import numpy as np
from scipy.special import gamma
import matplotlib.pyplot as plt

def chi2(x,n):
    return x**(n/2.0-1)*np.exp(-x/2.0)/(2**(n/2.0)*gamma(n/2.0))

xmax = 20; npt = 200
x = np.linspace(0,xmax,npt)

plt.plot(x,chi2(x,5),label = '$n = 3$')
plt.plot(x,chi2(x,9),label = '$n = 9$')
plt.plot(x,chi2(x,16),label = '$n = 16$')
plt.legend()