Plotting the beta distribution with different shapes

beta_distribution_graph.py

import numpy as np
from scipy.stats import beta
import matplotlib.pyplot as plt
plt.rcParams['figure.figsize'] = [10, 7]

# Bell shape
x = np.linspace(0, 1, 10000)
y1 = beta.pdf(x, 2, 8)
y2 = beta.pdf(x, 5, 5)
y3 = beta.pdf(x, 8, 2)

plt.title("PDF of Beta (Bell-shape)", fontsize=20)
plt.xlabel("X", fontsize=16)
plt.ylabel("Probability Density", fontsize=16)
plt.plot(x, y1, linewidth=3, color='firebrick')
plt.annotate("Beta(2,8)", xy=(0.15, 3.7), size = 14, ha='center', va='center', color='firebrick')
plt.plot(x, y2, linewidth=3, color='burlywood')
plt.annotate("Beta(5,5)", xy=(0.5, 2.6), size = 14, ha='center', va='center', color='burlywood')
plt.plot(x, y3, linewidth=3, color='dodgerblue')
plt.annotate("Beta(8,2)", xy=(0.85, 3.7), size = 14, ha='center', va='center', color='dodgerblue')
plt.ylim([0, 4])
plt.xlim([0, 1])
plt.show()

# Straight lines
x = np.linspace(0, 1, 10000)
y1 = beta.pdf(x, 1, 2)
y2 = beta.pdf(x, 1, 1)
y3 = beta.pdf(x, 2, 1)

plt.title("PDF of Beta (Straight lines)", fontsize=20)
plt.xlabel("X", fontsize=16)
plt.ylabel("Probability Density", fontsize=16)
plt.plot(x, y1, linewidth=3, color='firebrick')
plt.annotate("Beta(1,2)", xy=(0.88, 0.45), size = 14, ha='center', va='center', color='firebrick')
plt.plot(x, y2, linewidth=3, color='burlywood')
plt.annotate("Beta(1,1)", xy=(0.88, 1.15), size = 14, ha='center', va='center', color='burlywood')
plt.plot(x, y3, linewidth=3, color='dodgerblue')
plt.annotate("Beta(2,1)", xy=(0.88, 2.0), size = 14, ha='center', va='center', color='dodgerblue')
plt.ylim([0, 4])
plt.xlim([0, 1])
plt.show()

# U-shape
x = np.linspace(0, 1, 10000)
y1 = beta.pdf(x, 0.2, 0.8)
y2 = beta.pdf(x, 0.5, 0.5)
y3 = beta.pdf(x, 0.8, 0.2)

plt.title("PDF of Beta (U-shape)", fontsize=20)
plt.xlabel("X", fontsize=16)
plt.ylabel("Probability Density", fontsize=16)
plt.plot(x, y1, linewidth=3, color='firebrick')
plt.annotate("Beta(0.2,0.8)", xy=(0.85, 0.45), size = 14, ha='center', va='center', color='firebrick')
plt.plot(x, y2, linewidth=3, color='burlywood')
plt.annotate("Beta(0.5,0.5)", xy=(0.5, 0.88), size = 14, ha='center', va='center', color='burlywood')
plt.plot(x, y3, linewidth=3, color='dodgerblue')
plt.annotate("Beta(0.8,0.2)", xy=(0.15, 0.45), size = 14, ha='center', va='center', color='dodgerblue')
plt.ylim([0, 4])
plt.xlim([0, 1])
plt.show()