Sample transformation power.py

From Werner KRAUTH

Context

This page is part of my 2024 Beg Rohu Lectures on "The second Markov chain revolution" at the Summer School "Concepts and Methods of Statistical Physics" (3 - 15 June 2024).

Python program

import random, math
import matplotlib.pyplot as plt

N_trials = 1000000
data = []
gamma = -0.7
for iter in range(N_trials):
    Upsilon = random.uniform(0.0, 1.0)
#
#   This is the sample transformation SMAC eqs (1.28), (1.29)
#
    x = Upsilon ** (1.0 / (gamma + 1))
    data.append(x)

plt.title('power-law distribution (sample transformation)  $\gamma = $ '+ str(gamma))
plt.xlabel('$x$')
plt.ylabel('$\pi(x)$')
plt.hist(data, bins=100, density=True,label='data')
XValues = []
YValues = []
for i in range(5, 1000):
    x = i / 1000.0
    XValues.append(x)
    YValues.append((gamma + 1.0) * x ** gamma)
plt.plot(XValues, YValues, label='theory')
plt.legend(loc='upper right')
plt.show()