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Pull tutorial content out of example and into standalone tutorial.
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‎galleries/examples/statistics/histogram_normalization.py

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"""
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.. _histogram_normalization
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Histogram normalization
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=======================
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Histogram normalization rescales data into probabilities and therefore is a popular
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technique for comparing populations of different sizes or histograms computed using
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different bin edges. For more information on using `.Axes.hist` see
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:ref:`histogram_features`.
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Irregularly spaced bins
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-----------------------
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In this example, the bins below ``x=-1.25`` are six times wider than the rest of the
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bins ::
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dx = 0.1
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xbins = np.hstack([np.arange(-4, -1.25, 6*dx), np.arange(-1.25, 4, dx)])
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By normalizing by density, we preserve the shape of the distribution, whereas if we do
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not, then the wider bins have much higher counts than the thinner bins:
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"""
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import matplotlib.pyplot as plt
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import numpy as np
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rng = np.random.default_rng(19680801)
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xdata = rng.normal(size=1000)
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xpdf = np.arange(-4, 4, 0.1)
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pdf = 1 / (np.sqrt(2 * np.pi)) * np.exp(-xpdf**2 / 2)
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dx = 0.1
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xbins = np.hstack([np.arange(-4, -1.25, 6*dx), np.arange(-1.25, 4, dx)])
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fig, ax = plt.subplot_mosaic([['False', 'True']], layout='constrained')
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fig.suptitle("Histogram with irregularly spaced bins")
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ax['False'].hist(xdata, bins=xbins, density=False, histtype='step', label='Counts')
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ax['False'].plot(xpdf, pdf * len(xdata) * dx, label=r'$N\,f_X(x)\,\delta x_0$',
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alpha=.5)
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ax['True'].hist(xdata, bins=xbins, density=True, histtype='step', label='density')
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ax['True'].plot(xpdf, pdf, label='$f_X(x)$', alpha=.5)
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ax['False'].set(xlabel='x [V]', ylabel='Count per bin', title="density=False")
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# add the bin widths on the minor axes to highlight irregularity
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ax['False'].set_xticks(xbins, minor=True)
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ax['False'].legend()
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ax['True'].set(xlabel='x [$V$]', ylabel='Probability density [$V^{-1}$]',
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title="density=True")
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ax['False'].set_xticks(xbins, minor=True)
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ax['True'].legend()
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# %%
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# Different bin widths
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# --------------------
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#
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# Here we use normalization to compare histograms with binwidths of 0.1, 0.4, and 1.2:
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fig, ax = plt.subplot_mosaic([['False', 'True']], layout='constrained')
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fig.suptitle("Comparing histograms with different bin widths")
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# expected PDF
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ax['True'].plot(xpdf, pdf, '--', label='$f_X(x)$', color='k')
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for nn, dx in enumerate([0.1, 0.4, 1.2]):
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xbins = np.arange(-4, 4, dx)
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# expected histogram:
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ax['False'].plot(xpdf, pdf*1000*dx, '--', color=f'C{nn}', alpha=.5)
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ax['False'].hist(xdata, bins=xbins, density=False, histtype='step', label=dx)
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ax['True'].hist(xdata, bins=xbins, density=True, histtype='step')
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ax['False'].set(xlabel='x [$V$]', ylabel='Count per bin',
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title="density=False")
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ax['True'].set(xlabel='x [$V$]', ylabel='Probability density [$V^{-1}$]',
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title='density=True')
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ax['False'].legend(fontsize='small', title='bin width:')
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# %%
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# Populations of different sizes
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# ------------------------------
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#
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# Here we compare the distribution of ``xdata`` with a population of 1000, and
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# ``xdata2`` with 100 members. We demonstrate using *density* to generate the
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# probability density function(`pdf`_) and *weight* to generate an analog to the
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# probability mass function (`pmf`_).
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#
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# .. _pdf: https://en.wikipedia.org/wiki/Probability_density_function
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# .. _pmf: https://en.wikipedia.org/wiki/Probability_mass_function
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xdata2 = rng.normal(size=100)
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fig, ax = plt.subplot_mosaic([['no_norm', 'density', 'weight']], layout='constrained')
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fig.suptitle("Comparing histograms of populations of different sizes")
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xbins = np.arange(-4, 4, 0.25)
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for xd in [xdata, xdata2]:
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ax['no_norm'].hist(xd, bins=xbins, histtype='step')
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ax['density'].hist(xd, bins=xbins, histtype='step', density=True)
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ax['weight'].hist(xd, bins=xbins, histtype='step', weights=np.ones(len(xd))/len(xd),
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label=f'N={len(xd)}')
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ax['no_norm'].set(xlabel='x [$V$]', ylabel='Counts', title='No normalization')
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ax['density'].set(xlabel='x [$V$]',
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ylabel='Probability density [$V^{-1}$]', title='Density=True')
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ax['weight'].set(xlabel='x bins [$V$]', ylabel='Counts / N', title='Weight = 1/N')
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ax['weight'].legend(fontsize='small')
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plt.show()
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# %%
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#
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# .. tags:: plot type: histogram
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#
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# .. admonition:: References
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#
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# The use of the following functions, methods, classes and modules is shown
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# in this example:
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#
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# - `matplotlib.axes.Axes.hist` / `matplotlib.pyplot.hist`
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# - `matplotlib.axes.Axes.set`
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# - `matplotlib.axes.Axes.legend`
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#

‎galleries/tutorials/index.rst

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/tutorials/images
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/tutorials/lifecycle
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/tutorials/artists
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/tutorials/histogram_normalization
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.. only:: html
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- :ref:`arranging_axes`
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- :ref:`autoscale`
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- :ref:`imshow_extent`
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- :ref:`histogram_normalization`
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Advanced
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^^^^^^^^

‎galleries/tutorials/histogram_normalization.py renamed to ‎galleries/users_explain/artists/histogram_features.py

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