student-t.py

"""
    Code by Tae-Hwan Hung(@graykode)
    https://en.wikipedia.org/wiki/Student%27s_t-distribution
"""
import numpy as np
from matplotlib import pyplot as plt

def gamma_function(n):
    cal = 1
    for i in range(2, n):
        cal *= i
    return cal

def student_t(x, freedom, n):

    # divide [x.min(), x.max()] by n
    x = np.linspace(x.min(), x.max(), n)

    c = gamma_function((freedom + 1) // 2) \
        / np.sqrt(freedom * np.pi) * gamma_function(freedom // 2)
    y = c * (1 + x**2 / freedom) ** (-((freedom + 1) / 2))

    return x, y, np.mean(y), np.std(y)

for freedom in [1, 2, 5]:

    x = np.arange(-10, 10) # define range of x
    x, y, _, _ = student_t(x, freedom=freedom, n=10000)
    plt.plot(x, y, label=r'$v=%d$' % (freedom))

plt.legend()
plt.savefig('graph/student_t.png')
plt.show()