t-distribution.py

import numpy as np
from scipy.stats import t as student_t
from matplotlib import pyplot as plt
from matplotlib.backends.backend_pdf import PdfPages 

def student(n):
    samples = np.random.normal(0,1,n)
    mean = np.mean(samples)
    unbiased_var = np.var(samples, ddof=1)
    return np.sqrt(n/unbiased_var)*mean

n = 100
sample_size = 200000
samples = [student(n) for i in range(0,sample_size)]

fig = plt.figure()
plt.xlim([-10,10])

plt.title("$n="+str(n)+"$")
plt.xlabel("$x$")
plt.ylabel("$p(x)$")

plt.hist(samples,bins=2000,normed=True,range=(-100,100),label="histogram")

dist = student_t(n-1,0)
x = np.linspace(-10,10,200)
plt.plot(x, dist.pdf(x), alpha=0.7,label="p.d.f.")
plt.legend()
plt.show()
with PdfPages('n'+str(n)+'.pdf') as pp:
    # save figure
    pp.savefig(fig)