File:Bounded probability distributions, compared with the normal distribution.svg

import numpy as np import matplotlib.pyplot as plt

1. Define the distributions

def n(x):

   return np.exp(-0.5 * x**2) / np.sqrt(2 * np.pi)

def cosine(x):

   scos = 1.0 / np.sqrt(1/3.0 - 2/np.pi**2)
   return np.where(np.abs(x) > scos, 0, (1 + np.cos(x * np.pi / scos)) * 0.5 / scos)

def wigner(x):

   return np.where(np.abs(x) > 2, 0, np.sqrt(4 - x**2) * 0.5 / np.pi)

def uniform(x):

   return np.where(np.abs(x) > np.sqrt(3), 0, 0.5 / np.sqrt(3))

1. Create x-axis values

x = np.linspace(-4, 4, 200)

1. Calculate y-axis values for each distribution

y_n = n(x) y_cosine = cosine(x) y_wigner = wigner(x) y_uniform = uniform(x)

1. Plot the distributions

plt.figure(figsize=(12, 10)) plt.plot(x, y_n, label='Normal (Kurtosis: 0)') plt.plot(x, y_cosine, label='Raised Cosine (Kurtosis: -0.59)') plt.plot(x, y_wigner, label='Wigner Semicircle (Kurtosis: -1)') plt.plot(x, y_uniform, label='Uniform (Kurtosis: -1.2)')

1. Add legend and labels

plt.legend() plt.xlabel('x') plt.ylabel('Probability Density') plt.title('Some Bounded Distributions')

plt.savefig('some_bounded_distributions.svg')