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DOC: MEP12 docstring for the histogram examples
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‎examples/statistics/histogram_demo_cumulative.py

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"""
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Demo of the histogram (hist) function used to plot a cumulative distribution.
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"""Demo of using histograms to plot a cumulative distribution.
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This shows how to plot a cumulative, normalized histogram as a
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step function as means of visualization the empirical cumulative
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distribution function (CDF) of a sample. We also use the `mlab`
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module to show the theoretical CDF.
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A couple of other options to the `hist` function are demostrated.
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Namely, we use the `normed` parameter to normalize the histogram and
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a couple of different options to the `cumulative` parameter. Normalizing
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a histogram means that the counts within each bin are scaled such that
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the total height of each bin sum up to 1. Since we're showing the
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cumulative histogram, the max value at the end of the series is 1.
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The `normed` parameter takes a boolean value.
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The `cumulative` kwarg is a little more nuanced. Like `normed`, you can
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pass it True or False, but you can also pass it -1 and that will
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reverse the distribution. In engineering, CDFs where `cumulative` is
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simply True are sometimes "non-excedance" curves. In other words, you
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can look at the y-value to set the probability of excedance. For example
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the value of 225 on the x-axis corresponse to about 0.85 on the y-axis,
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so there's an 85% chance that an observation in the sames does not
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exceed 225.
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Conversely, setting, `cumulative` to -1 as is done in the last series
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for this example, creates a "excedance" curve.
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"""
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import numpy as np
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import matplotlib.pyplot as plt
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from matplotlib import mlab
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np.random.seed(0)
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mu = 200
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sigma = 25
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n_bins = 50
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x = mu + sigma*np.random.randn(10000)
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x = mu + sigma*np.random.randn(100)
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n, bins, patches = plt.hist(x, n_bins, normed=1,
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histtype='step', cumulative=True)
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fig, ax = plt.subplots(figsize=(8, 4))
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# plot the cumulative histograme
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n, bins, patches = ax.hist(x, n_bins, normed=1, histtype='step',
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cumulative=True, label='Empirical')
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# Add a line showing the expected distribution.
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y = mlab.normpdf(bins, mu, sigma).cumsum()
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y /= y[-1]
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plt.plot(bins, y, 'k--', linewidth=1.5)
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ax.plot(bins, y, 'k--', linewidth=1.5, label='Theoretical')
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# Overlay a reversed cumulative histogram.
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plt.hist(x, bins=bins, normed=1, histtype='step', cumulative=-1)
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ax.hist(x, bins=bins, normed=1, histtype='step', cumulative=-1,
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label='Reversed emp.')
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plt.grid(True)
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plt.title('cumulative step')
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# tidy up the figure
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ax.grid(True)
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ax.legend(loc='right')
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ax.set_title('Cumulative step histograms')
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ax.set_xlabel('Annual rainfall (mm)')
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ax.set_ylabel('Likelihood of occurance')
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plt.show()

‎examples/statistics/histogram_demo_features.py

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"""
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Demo of the histogram (hist) function with a few features.
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"""Demo of the histogram (hist) function with a few features.
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In addition to the basic histogram, this demo shows a few optional features:
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In addition to the basic histogram, this demo shows a few optional
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features:
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* Setting the number of data bins
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* The ``normed`` flag, which normalizes bin heights so that the integral of
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the histogram is 1. The resulting histogram is a probability density.
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* The ``normed`` flag, which normalizes bin heights so that the
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integral of the histogram is 1. The resulting histogram is an
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approximation of the probability density function.
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* Setting the face color of the bars
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* Setting the opacity (alpha value).
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"""
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import numpy as np
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import matplotlib.mlab as mlab
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import matplotlib.pyplot as plt
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np.random.seed(0)
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# example data
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mu = 100 # mean of distribution
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sigma = 15 # standard deviation of distribution
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x = mu + sigma * np.random.randn(10000)
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x = mu + sigma * np.random.randn(437)
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num_bins = 50
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fig, ax = plt.subplots()
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# the histogram of the data
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n, bins, patches = plt.hist(x, num_bins, normed=1)
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n, bins, patches = ax.hist(x, num_bins, normed=1)
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# add a 'best fit' line
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y = mlab.normpdf(bins, mu, sigma)
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plt.plot(bins, y, '--')
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plt.xlabel('Smarts')
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plt.ylabel('Probability density')
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plt.title(r'Histogram of IQ: $\mu=100$, $\sigma=15$')
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ax.plot(bins, y, '--')
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ax.set_xlabel('Smarts')
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ax.set_ylabel('Probability density')
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ax.set_title(r'Histogram of IQ: $\mu=100$, $\sigma=15$')
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# Tweak spacing to prevent clipping of ylabel
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plt.subplots_adjust(left=0.15)
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fig.tight_layout()
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plt.show()

‎examples/statistics/histogram_demo_histtypes.py

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"""
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Demo of the histogram (hist) function with different ``histtype`` settings.
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"""Demo of the histogram function's different ``histtype`` settings.
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* Histogram with step curve that has a color fill.
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* Histogram with with unequal bin widths.
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* Histogram with custom and unequal bin widths.
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"""
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import numpy as np
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import matplotlib.pyplot as plt
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np.random.seed(0)
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mu = 200
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sigma = 25
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x = mu + sigma*np.random.randn(10000)
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x = np.random.normal(mu, sigma, size=100)
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fig, (ax0, ax1) = plt.subplots(ncols=2, figsize=(8, 4))
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ax1.hist(x, bins, normed=1, histtype='bar', rwidth=0.8)
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ax1.set_title('unequal bins')
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plt.tight_layout()
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fig.tight_layout()
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plt.show()

‎examples/statistics/histogram_demo_multihist.py

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"""
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Demo of the histogram (hist) function with multiple data sets.
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"""Demo of the histogram (hist) function with multiple data sets.
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Plot histogram with multiple sample sets and demonstrate:
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* Use of legend with multiple sample sets
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* Stacked bars
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* Step curve with a color fill
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* Step curve with no fill
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* Data sets of different sample sizes
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"""
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import numpy as np
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import matplotlib.pyplot as plt
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np.random.seed(0)
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n_bins = 10
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x = np.random.randn(1000, 3)
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fig, axes = plt.subplots(nrows=2, ncols=2)
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ax0, ax1, ax2, ax3 = axes.flat
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ax0, ax1, ax2, ax3 = axes.flatten()
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colors = ['red', 'tan', 'lime']
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ax0.hist(x, n_bins, normed=1, histtype='bar', color=colors, label=colors)
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ax1.hist(x, n_bins, normed=1, histtype='bar', stacked=True)
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ax1.set_title('stacked bar')
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ax2.hist(x, n_bins, histtype='step', stacked=True, fill=True)
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ax2.set_title('stepfilled')
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ax2.hist(x, n_bins, histtype='step', stacked=True, fill=False)
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ax2.set_title('step (unfilled)')
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# Make a multiple-histogram of data-sets with different length.
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x_multi = [np.random.randn(n) for n in [10000, 5000, 2000]]
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ax3.hist(x_multi, n_bins, histtype='bar')
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ax3.set_title('different sample sizes')
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plt.tight_layout()
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fig.tight_layout()
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plt.show()

‎examples/statistics/multiple_histograms_side_by_side.py

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"""
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Demo of how to produce multiple histograms side by side
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"""Demo of how to produce multiple histograms side by side
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This example plots horizonal histograms of different samples along
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a categorical x-axis. Additionally, the histograms are plotted to
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be symmetrical about their x-position, thus making them very similar
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to violin plots.
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To make this highly specialized plot, we can't use the standard `hist`
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method. Instead we use `barh` to draw the horizontal bars directly. The
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vertical positions and lengths of the bars are computed via the
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`np.histogram` function. The histograms for all the samples are
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computed using the same range (min and max values) and number of bins,
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so that the bins for each sample are in the same vertical positions.
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"""
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import numpy as np
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import matplotlib.pyplot as plt
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np.random.seed(0)
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number_of_bins = 20
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# An example of three data sets to compare
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number_of_data_points = 1000
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number_of_data_points = 387
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labels = ["A", "B", "C"]
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data_sets = [np.random.normal(0, 1, number_of_data_points),
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np.random.normal(6, 1, number_of_data_points),
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np.random.normal(-3, 1, number_of_data_points)]
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# Computed quantities to aid plotting
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hist_range = (np.min(data_sets), np.max(data_sets))
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binned_data_sets = [np.histogram(d, range=hist_range, bins=number_of_bins)[0]
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for d in data_sets]
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binned_data_sets = [
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np.histogram(d, range=hist_range, bins=number_of_bins)[0]
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for d in data_sets
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]
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binned_maximums = np.max(binned_data_sets, axis=1)
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x_locations = np.arange(0, sum(binned_maximums), np.max(binned_maximums))
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# The bin_edges are the same for all of the histograms
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bin_edges = np.linspace(hist_range[0], hist_range[1], number_of_bins + 1)
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centers = .5 * (bin_edges + np.roll(bin_edges, 1))[:-1]
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centers = 0.5 * (bin_edges + np.roll(bin_edges, 1))[:-1]
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heights = np.diff(bin_edges)
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# Cycle through and plot each histogram
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ax = plt.subplot(111)
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fig, ax = plt.subplots()
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for x_loc, binned_data in zip(x_locations, binned_data_sets):
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lefts = x_loc - .5 * binned_data
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lefts = x_loc - 0.5 * binned_data
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ax.barh(centers, binned_data, height=heights, left=lefts)
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ax.set_xticks(x_locations)

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