central limit theorem definition code example

Example: central limit theorem python example

import numpy as npimport matplotlib.pyplot as pltdef repeat_sample_draws_exponential(n, samp_size, mu, show_all=False):    means = []    samples = []    for ii in range(0, n):        samples.append(np.random.exponential(mu, samp_size))        means.append(np.mean(samples[ii]))    if show_all:        pltdim = np.math.ceil(np.math.sqrt(n))        fig, axs = plt.subplots(pltdim, pltdim, figsize=(8, 8), gridspec_kw={'hspace': 0.2}, sharex=True, sharey=True)        fig.suptitle('Individual Samples\' Order Value Distribution')        fig.text(0.5, 0.04, 'Order Values ($)', ha='center')        fig.text(0.04, 0.5, 'Number of Customers', ha='center', rotation='vertical')        axs = axs.flatten()        for ii in range(0, n):            plt.sca(axs[ii])            plt.gca().hist(samples[ii], bins=int(50), histtype='step',                           label='$mean = {0:.2f}$'.format(np.mean(samples[ii])), range=[0, 2 * mu])            if n < 10:                plt.gca().set_title('Sample #{0} : average={1:.2f}'.format(ii, np.mean(samples[ii])))            for item in ([axs[ii].title, axs[ii].xaxis.label, axs[ii].yaxis.label] +                             axs[ii].get_xticklabels() + axs[ii].get_yticklabels()):                item.set_fontsize(8)        plt.savefig('expdist_{0}_mu_{1}_sample_{2}_sampsize'.format(mu, n, samp_size))    plt.clf()    plt.hist(means, bins=int(10), histtype='step')    plt.title('Overall Average of {} Samples\' Average Order Value'.format(n))    plt.xlabel('Average of Individual Sample\'s Order Value ($)')    plt.savefig('average_of_expdist_{0}_mu_{1}_sample_{2}_sampsize'.format(mu, n, samp_size))    print('mean of the samples is {0:.2f}'.format(np.mean(means)))    print('standard deviation of the samples is {0:.2f}'.format(np.std(means)))repeat_sample_draws_exponential(100, 1000, 170, True)