import numpy as np import numpy.random as npr import matplotlib.pyplot as plt # make plots look like R plt.style.use('ggplot') plt.rc('axes', facecolor='white', edgecolor='black', axisbelow=True, grid=False) # set the size of the simulated populations size = 5000 # randomly generating a set of population distributions, some very non-normal distributions = [ npr.normal(1, 10, size=size), npr.gamma(2, 1, size=size), np.concatenate( (npr.normal(1, 2, size=size), npr.normal(10, 1.5, size=size)) ), npr.hypergeometric(5, 20, 5, size=size), npr.uniform(size=size), npr.choice([1,2,3,4,5,6], p = [8/36, 4/36, 2/36, 9/36, 10/36, 3/36], size = size) ] # set the number of samples to draw, and some different sample sizes n_iters = 1000 samp_size = 20 samp_size_big = 100 samp_size_bigger = 500 # lists in which to store the distributions of sample means samp_ds = [] samp_ds_big = [] samp_ds_bigger = [] # repeatedly drawing samples of different sizes from each distribution for dist in distributions: # arrays to store the sample means samp_d = np.zeros(n_iters) samp_d_big = np.zeros(n_iters) samp_d_bigger = np.zeros(n_iters) for i in np.arange(n_iters): # drawing samples of one size sample = np.random.choice(dist, size=samp_size) samp_d[i] = np.mean(sample) # drawing samples of another size, bigger than the first sample_big = np.random.choice(dist, size=samp_size_big) samp_d_big[i] = np.mean(sample_big) # drawing samples of another size, bigger than the others sample_bigger = np.random.choice(dist, size=samp_size_bigger) samp_d_bigger[i] = np.mean(sample_bigger) samp_ds.append(samp_d) samp_ds_big.append(samp_d_big) samp_ds_bigger.append(samp_d_bigger) # plotting the original population distributions, each next row of the plot is the sampling distribution of the mean # for samples of a certain size drawn from each population. The x axis of later plots is coerced to be the same length # as that from earlier plots, to show the increasing precision of the sampling distribution. fig1, axes1 = plt.subplots(1, 6, figsize = (16, 4)) fig2, axes2 = plt.subplots(1, 6, figsize = (16, 4)) fig3, axes3 = plt.subplots(1, 6, figsize = (16, 4)) fig4, axes4 = plt.subplots(1, 6, figsize = (16, 4)) colors = ['red', 'blue', 'orange', 'cyan', 'green', 'grey'] for ax1, ax2, ax3, ax4, dist, samp_d, samp_d_big, samp_d_bigger, color in zip( axes1, axes2, axes3, axes4, distributions, samp_ds, samp_ds_big, samp_ds_bigger, colors): ax1.hist(dist, color=color, bins = 15) ax1.set_yticklabels([]) ax1.set_xticklabels([]) ax2.hist(samp_d, color=color, bins = 15) ax2.set_yticklabels([]) ax2.set_xticklabels([]) ax3.hist(samp_d_big, color=color, bins = 15) ax3.set_xlim(ax2.get_xlim()) ax3.set_yticklabels([]) ax3.set_xticklabels([]) ax4.hist(samp_d_bigger, color=color, bins = 15) ax4.set_xlim(ax2.get_xlim()) ax4.set_yticklabels([]) ax4.set_xticklabels([]) # label the plot fig1.suptitle('Some population distributions:') fig2.suptitle('Distribution of the means of ' f'{n_iters} samples drawn from each population, sample size == {samp_size}:') fig3.suptitle('Distribution of the means of ' f'{n_iters} samples drawn from each population, sample size == {samp_size_big}:') fig4.suptitle('Distribution of the means of ' f'{n_iters} samples drawn from each population, sample size == {samp_size_bigger}:');