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pylab_examples example code: boxplot_demo2.pyΒΆ

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../../_images/boxplot_demo2.png
"""
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, ax1 = plt.subplots(figsize=(10,6))
fig.canvas.set_window_title('A Boxplot Example')
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 horizontal 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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