Sample transformation exp.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 = 100000
data = []
lam = 2.7
for iter in range(N_trials):
    Upsilon = random.uniform(0.0, 1.0)
#
#   This is the sample transformation SMAC eqs (1.30), (1.31)
#
    x = -math.log(Upsilon) / lam
    data.append(x)

plt.title('exponential random numbers (sample transformation) $\lambda = $ '+ str(lam))
plt.xlabel('$x$')
plt.ylabel('$\pi(x)$')
plt.hist(data, bins=100, density=True,label='data')
XValues = []
YValues = []
for i in range(1000):
    x = i / 200.0
    XValues.append(x)
    YValues.append(lam * math.exp(-lam * x))
plt.plot(XValues, YValues, label='theory')
plt.legend(loc='upper right')
plt.show()