"""
Thanks Josh Hemann for the example
"""
import numpy as np
import matplotlib.pyplot as plt
from matplotlib.patches import Polygon
# Generate some data from five different probability distributions,
# each with different characteristics. We want to play with how an IID
# bootstrap resample of the data preserves the distributional
# properties of the original sample, and a boxplot is one visual tool
# to make this assessment
numDists = 5
randomDists = ['Normal(1,1)',' Lognormal(1,1)', 'Exp(1)', 'Gumbel(6,4)',
'Triangular(2,9,11)']
N = 500
norm = np.random.normal(1,1, N)
logn = np.random.lognormal(1,1, N)
expo = np.random.exponential(1, N)
gumb = np.random.gumbel(6, 4, N)
tria = np.random.triangular(2, 9, 11, N)
# Generate some random indices that we'll use to resample the original data
# arrays. For code brevity, just use the same random indices for each array
bootstrapIndices = np.random.random_integers(0, N-1, N)
normBoot = norm[bootstrapIndices]
expoBoot = expo[bootstrapIndices]
gumbBoot = gumb[bootstrapIndices]
lognBoot = logn[bootstrapIndices]
triaBoot = tria[bootstrapIndices]
data = [norm, normBoot, logn, lognBoot, expo, expoBoot, gumb, gumbBoot,
tria, triaBoot]
fig = plt.figure(figsize=(10,6))
fig.canvas.set_window_title('A Boxplot Example')
ax1 = fig.add_subplot(111)
plt.subplots_adjust(left=0.075, right=0.95, top=0.9, bottom=0.25)
bp = plt.boxplot(data, notch=0, sym='+', vert=1, whis=1.5)
plt.setp(bp['boxes'], color='black')
plt.setp(bp['whiskers'], color='black')
plt.setp(bp['fliers'], color='red', marker='+')
# Add a horizontal grid to the plot, but make it very light in color
# so we can use it for reading data values but not be distracting
ax1.yaxis.grid(True, linestyle='-', which='major', color='lightgrey',
alpha=0.5)
# Hide these grid behind plot objects
ax1.set_axisbelow(True)
ax1.set_title('Comparison of IID Bootstrap Resampling Across Five Distributions')
ax1.set_xlabel('Distribution')
ax1.set_ylabel('Value')
# Now fill the boxes with desired colors
boxColors = ['darkkhaki','royalblue']
numBoxes = numDists*2
medians = range(numBoxes)
for i in range(numBoxes):
box = bp['boxes'][i]
boxX = []
boxY = []
for j in range(5):
boxX.append(box.get_xdata()[j])
boxY.append(box.get_ydata()[j])
boxCoords = zip(boxX,boxY)
# Alternate between Dark Khaki and Royal Blue
k = i % 2
boxPolygon = Polygon(boxCoords, facecolor=boxColors[k])
ax1.add_patch(boxPolygon)
# Now draw the median lines back over what we just filled in
med = bp['medians'][i]
medianX = []
medianY = []
for j in range(2):
medianX.append(med.get_xdata()[j])
medianY.append(med.get_ydata()[j])
plt.plot(medianX, medianY, 'k')
medians[i] = medianY[0]
# Finally, overplot the sample averages, with horixzontal alignment
# in the center of each box
plt.plot([np.average(med.get_xdata())], [np.average(data[i])],
color='w', marker='*', markeredgecolor='k')
# Set the axes ranges and axes labels
ax1.set_xlim(0.5, numBoxes+0.5)
top = 40
bottom = -5
ax1.set_ylim(bottom, top)
xtickNames = plt.setp(ax1, xticklabels=np.repeat(randomDists, 2))
plt.setp(xtickNames, rotation=45, fontsize=8)
# Due to the Y-axis scale being different across samples, it can be
# hard to compare differences in medians across the samples. Add upper
# X-axis tick labels with the sample medians to aid in comparison
# (just use two decimal places of precision)
pos = np.arange(numBoxes)+1
upperLabels = [str(np.round(s, 2)) for s in medians]
weights = ['bold', 'semibold']
for tick,label in zip(range(numBoxes),ax1.get_xticklabels()):
k = tick % 2
ax1.text(pos[tick], top-(top*0.05), upperLabels[tick],
horizontalalignment='center', size='x-small', weight=weights[k],
color=boxColors[k])
# Finally, add a basic legend
plt.figtext(0.80, 0.08, str(N) + ' Random Numbers' ,
backgroundcolor=boxColors[0], color='black', weight='roman',
size='x-small')
plt.figtext(0.80, 0.045, 'IID Bootstrap Resample',
backgroundcolor=boxColors[1],
color='white', weight='roman', size='x-small')
plt.figtext(0.80, 0.015, '*', color='white', backgroundcolor='silver',
weight='roman', size='medium')
plt.figtext(0.815, 0.013, ' Average Value', color='black', weight='roman',
size='x-small')
plt.show()
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