%pylab inline

import numpy as np
import matplotlib.pyplot as plt

import scipy.stats

t_dist = scipy.stats.t
norm_dist = scipy.stats.norm

x_values = np.linspace(-4, 4, 100)

t_prob_3 = t_dist.pdf(x_values, 3)
t_prob_10 = t_dist.pdf(x_values, 10)
t_prob_40 = t_dist.pdf(x_values, 40)
z_prob = norm_dist.pdf(x_values)

plt.figure(figsize=(10, 8))
plt.plot(x_values, t_prob_3, 'r:', label='t df=3')
plt.plot(x_values, t_prob_10, 'g:', label='t df=10')
plt.plot(x_values, t_prob_40, 'b:', label='t df=40')
plt.plot(x_values, z_prob, 'k', label='z')
plt.xlabel('$z$ or $t$ value')
plt.ylabel('probability')
plt.legend()

t_cdf_10 = t_dist.cdf(x_values, 10)
plt.figure(figsize=(10, 8))
plt.plot(x_values, t_cdf_10, 'b', label='t cdf df=10')
plt.plot(x_values, t_prob_10, 'k', label='t pdf df=10')
plt.xlabel('$z$ or $t$ value')
plt.ylabel('probability')
plt.legend()

p = t_dist.cdf(2, 10)
p

t_dist.ppf(p, 10)

t_for_05 = t_dist.ppf(0.95, 10)
t_for_05

p_sf = t_dist.sf(2, 10)
p_sf

1 - t_dist.cdf(2, 10)

t_dist.isf(p_sf, 10)

norm_dist.cdf(0.9)

norm_dist.ppf(0.95)