"""
==========================================================
Demo of using histograms to plot a cumulative distribution
==========================================================

This shows how to plot a cumulative, normalized histogram as a
step function in order to visualize the empirical cumulative
distribution function (CDF) of a sample. We also use the ``mlab``
module to show the theoretical CDF.

A couple of other options to the ``hist`` function are demonstrated.
Namely, we use the ``normed`` parameter to normalize the histogram and
a couple of different options to the ``cumulative`` parameter.
The ``normed`` parameter takes a boolean value. When ``True``, the bin
heights are scaled such that the total area of the histogram is 1. The
``cumulative`` kwarg is a little more nuanced. Like ``normed``, you
can pass it True or False, but you can also pass it -1 to reverse the
distribution.

Since we're showing a normalized and cumulative histogram, these curves
are effectively the cumulative distribution functions (CDFs) of the
samples. In engineering, empirical CDFs are sometimes called
"non-exceedance" curves. In other words, you can look at the
y-value for a given-x-value to get the probability of and observation
from the sample not exceeding that x-value. For example, the value of
225 on the x-axis corresponds to about 0.85 on the y-axis, so there's an
85% chance that an observation in the sample does not exceed 225.
Conversely, setting, ``cumulative`` to -1 as is done in the
last series for this example, creates a "exceedance" curve.

Selecting different bin counts and sizes can significantly affect the
shape of a histogram. The Astropy docs have a great section on how to
select these parameters:
http://docs.astropy.org/en/stable/visualization/histogram.html

"""

import numpy as np
import matplotlib.pyplot as plt
from matplotlib import mlab

np.random.seed(0)

mu = 200
sigma = 25
n_bins = 50
x = np.random.normal(mu, sigma, size=100)

fig, ax = plt.subplots(figsize=(8, 4))

# plot the cumulative histogram
n, bins, patches = ax.hist(x, n_bins, normed=1, histtype='step',
                           cumulative=True, label='Empirical')

# Add a line showing the expected distribution.
y = mlab.normpdf(bins, mu, sigma).cumsum()
y /= y[-1]

ax.plot(bins, y, 'k--', linewidth=1.5, label='Theoretical')

# Overlay a reversed cumulative histogram.
ax.hist(x, bins=bins, normed=1, histtype='step', cumulative=-1,
        label='Reversed emp.')

# tidy up the figure
ax.grid(True)
ax.legend(loc='right')
ax.set_title('Cumulative step histograms')
ax.set_xlabel('Annual rainfall (mm)')
ax.set_ylabel('Likelihood of occurrence')

plt.show() 

　

Traceback (most recent call last):
  File "M:\______\histogram_demo_cumulative.py", line 52, in 
    n, bins, patches = ax.hist(x, n_bins, normed=1, histtype='step',
                       ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "C:\Users\______\AppData\Local\Programs\Python\Python311\Lib
    \site-packages\matplotlib\__init__.py", line 1459, in inner
    return func(ax, *map(sanitize_sequence, args), **kwargs)
           ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "C:\Users\______\AppData\Local\Programs\Python\Python311\Lib
    \site-packages\matplotlib\axes\_axes.py", line 6943, in hist
    p._internal_update(kwargs)
  File "C:\Users\______\AppData\Local\Programs\Python\Python311\Lib
    \site-packages\matplotlib\artist.py", line 1223, in _internal_update
    return self._update_props(
           ^^^^^^^^^^^^^^^^^^^
  File "C:\Users\______\AppData\Local\Programs\Python\Python311\Lib
    \site-packages\matplotlib\artist.py", line 1197, in _update_props
    raise AttributeError(
AttributeError: Polygon.set() got an unexpected keyword argument 'normed' 

Traceback (most recent call last):
  File "E:\______\histogram_demo_cumulative.py", line 52, in 
    n, bins, patches = ax.hist(x, n_bins, normed=1, histtype='step',
                       ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "C:\Program Files\Python312\Lib\site-packages\matplotlib\__init__.py", 
    line 1478, in inner
    return func(ax, *map(sanitize_sequence, args), **kwargs)
           ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "C:\Program Files\Python312\Lib\site-packages\matplotlib\axes\_axes.py", 
    line 7012, in hist
    p._internal_update(kwargs)
  File "C:\Program Files\Python312\Lib\site-packages\matplotlib\artist.py", 
    line 1219, in _internal_update
    return self._update_props(
           ^^^^^^^^^^^^^^^^^^^
  File "C:\Program Files\Python312\Lib\site-packages\matplotlib\artist.py", 
    line 1193, in _update_props
    raise AttributeError(
AttributeError: Polygon.set() got an unexpected keyword argument 'normed' 

"""
=================================
Plotting cumulative distributions
=================================

This example shows how to plot the empirical cumulative distribution function
(ECDF) of a sample. We also show the theoretical CDF.

In engineering, ECDFs are sometimes called "non-exceedance" curves: the y-value
for a given x-value gives probability that an observation from the sample is
below that x-value. For example, the value of 220 on the x-axis corresponds to
about 0.80 on the y-axis, so there is an 80% chance that an observation in the
sample does not exceed 220. Conversely, the empirical *complementary*
cumulative distribution function (the ECCDF, or "exceedance" curve) shows the
probability y that an observation from the sample is above a value x.

A direct method to plot ECDFs is `.Axes.ecdf`.  Passing ``complementary=True``
results in an ECCDF instead.

Alternatively, one can use ``ax.hist(data, density=True, cumulative=True)`` to
first bin the data, as if plotting a histogram, and then compute and plot the
cumulative sums of the frequencies of entries in each bin.  Here, to plot the
ECCDF, pass ``cumulative=-1``.  Note that this approach results in an
approximation of the E(C)CDF, whereas `.Axes.ecdf` is exact.
"""

import matplotlib.pyplot as plt
import numpy as np

np.random.seed(19680801)

mu = 200
sigma = 25
n_bins = 25
data = np.random.normal(mu, sigma, size=100)

fig = plt.figure(figsize=(9, 4), layout="constrained")
axs = fig.subplots(1, 2, sharex=True, sharey=True)

# Cumulative distributions.
axs[0].ecdf(data, label="CDF")
n, bins, patches = axs[0].hist(data, n_bins, density=True, histtype="step",
                               cumulative=True, label="Cumulative histogram")
x = np.linspace(data.min(), data.max())
y = ((1 / (np.sqrt(2 * np.pi) * sigma)) *
     np.exp(-0.5 * (1 / sigma * (x - mu))**2))
y = y.cumsum()
y /= y[-1]
axs[0].plot(x, y, "k--", linewidth=1.5, label="Theory")

# Complementary cumulative distributions.
axs[1].ecdf(data, complementary=True, label="CCDF")
axs[1].hist(data, bins=bins, density=True, histtype="step", cumulative=-1,
            label="Reversed cumulative histogram")
axs[1].plot(x, 1 - y, "k--", linewidth=1.5, label="Theory")

# Label the figure.
fig.suptitle("Cumulative distributions")
for ax in axs:
    ax.grid(True)
    ax.legend()
    ax.set_xlabel("Annual rainfall (mm)")
    ax.set_ylabel("Probability of occurrence")
    ax.label_outer()

plt.show()

# %%
#
# .. admonition:: References
#
#    The use of the following functions, methods, classes and modules is shown
#    in this example:
#
#    - `matplotlib.axes.Axes.hist` / `matplotlib.pyplot.hist`
#    - `matplotlib.axes.Axes.ecdf` / `matplotlib.pyplot.ecdf` 

Traceback (most recent call last):
  File "M:\______\histogram_cumulative_2.py", line 41, in 
    axs[0].ecdf(data, label="CDF")
    ^^^^^^^^^^^
AttributeError: 'Axes' object has no attribute 'ecdf' 

Python 3.12.0 (matplotlib 3.8.1) では、正常実行です。

　

• 2023/12/10 Ver=1.04 Python 3.12.0 (matplotlib 3.8.1)で確認
• 2023/12/10 Ver=1.04 Python 3.11.6 (matplotlib 3.7.1)で確認
• 2023/04/05 Ver=1.03 Python 3.11.2 で確認
• 2020/11/02 Ver=1.01 Python 3.7.8 で確認
• 2018/12/06 Ver=1.01 初版リリース

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