Now that we’ve seen both the standard normal distribution and a t-distribution with a single degree of freedom, let’s plot them together to see how they compare.

# Library imports

import numpy as np

import seaborn as sns

import scipy.stats as stats

import matplotlib.pyplot as plt

%matplotlib inline

# Normal distribution

x = np.linspace(-4, 4, 500)

y = stats.norm.pdf(x)

# T distribution

df = 1

y_t = stats.t.pdf(x, df)

# Plotting

plt.ylabel('Probability Density')

plt.xlabel('Standard Deviations')

plt.plot(x, y, color='blue', label='Normal Dist.')

plt.plot(x, y_t, color='green', label=f'T-Dist., df={df}')

plt.legend()

# Styling - optional

sns.set_context('notebook')

sns.despine()

import matplotlib.pyplot as plt

import numpy as np

from scipy.stats import t

x = np.linspace(-5, 5, 100)

degrees_of_freedom = [1, 2, 5, 10]  # Varying degrees of freedom

# Plotting T-distribution curves for different degrees of freedom

for df in reversed(degrees_of_freedom):

    y = t.pdf(x, df)  # Using default location and scale parameters (0 and 1)

    plt.plot(x, y, label=f"Degrees of Freedom = {df}")

plt.xlabel('x')

plt.ylabel('PDF')

plt.title('T-Distribution with Varying Degrees of Freedom')

plt.legend()

plt.show()