Demonstrates how to sample from exponential and gaussian distributions using only a uniform distribution (useful for languages like PHP with no built-in statistical sampling libraries).

sample_uniform.py

import numpy as np
import matplotlib.pyplot as plot
import sys

def exp(mean, samples = 100):
    y = []
    lambda_param = (1 / mean)
    for i in range(0, samples):
        rand = np.random.rand()
        y.append(np.log(1 - rand) / (-1.0 * lambda_param))

    plot.hist(y, bins = 100)
    plot.show()

def normal(mean = 0, stddev = 1, samples = 100):
    y = []
    for i in range(0, samples):
        rand1 = np.random.rand()
        rand2 = np.random.rand()
        var = np.sqrt(-2 * np.log(rand1)) * np.cos(2 * np.pi * rand2)
        y.append((var * stddev) + mean)
    plot.hist(y, bins = 100)
    plot.show()

normal(mean = 40, stddev = 1, samples = 10000)