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 import matplotlib.pyplot as plt import random from random import seed from statistics import * from scipy.stats import norm
def z_n_calc(n): root_n = pow(n, 0.5) seed() num_array = [random.uniform(0,1) for _ in range(n)] expectation = sum(num_array)/n stdeviation = stdev(num_array) res = 0 for i in range(0, n): res = res + (num_array[i]expectation)/(stdeviation*root_n)
return res
def sample_generator(n): return [z_n_calc(n) for _ in range(10000)]
def norm_cdf_generator(array_in): return [norm.cdf(x) for x in array_in] y_array = [x/10000.0 for x in range(10000)]
x_array_10 = sorted(sample_generator(10)) plt.figure()
plt.plot(x_array_10, y_array, label='Z_10') plt.plot(x_array_10, norm_cdf_generator(x_array_10)) plt.legend()
x_array_100 = sorted(sample_generator(100)) plt.figure()
plt.plot(x_array_100, y_array, label='Z_100') plt.plot(x_array_100, norm_cdf_generator(x_array_100)) plt.legend()
x_array_1000 = sorted(sample_generator(1000)) plt.figure() plt.plot(x_array_1000, y_array, label='Z_1000') plt.plot(x_array_1000, norm_cdf_generator(x_array_1000)) plt.legend()
plt.figure() plt.plot(x_array_10, y_array, label='Z_10') plt.plot(x_array_100, y_array, label='Z_100') plt.plot(x_array_1000, y_array, label='Z_1000') plt.plot(x_array_1000, norm_cdf_generator(x_array_10), label='Standard normal') plt.legend()
plt.ylabel('CDF') plt.show()
