Generate normally-distributed random samples from uniform samples by rejection sampling

rejection_sampling.py

import numpy as np
import matplotlib.pyplot as plt 
import bisect
from scipy import stats

rng = np.random.default_rng()
desired_variance = 1
desired_mean = 0
uni_rand = rng.uniform(low=-desired_variance*3, high=desired_variance*3, size=1000)
_ = plt.hist(uni_rand, bins='auto')
plt.show()

bins_edges = np.linspace(start=-desired_variance*3, stop=desired_variance*3, num=100)
bins_centers = (bins_edges[0:-1] + bins_edges[1:]) / 2
desired_bin_density = stats.norm(desired_mean, desired_variance).pdf(bins_centers)

for i in range(10000):
    uni_rand_candidate = rng.uniform(low=-desired_variance*3, high=desired_variance*3)
    candidate_bin = bisect.bisect(bins_edges, uni_rand_candidate) - 1
    bin_counts, _ = np.histogram(uni_rand, bins=bins_edges, density=True)
    if bin_counts[candidate_bin] < desired_bin_density[candidate_bin]:
        uni_rand = np.append(uni_rand, uni_rand_candidate)
        
_ = plt.hist(uni_rand, bins='auto')
plt.show()