bpo-36546: Add statistics.quantiles() (#12710)
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@ -48,6 +48,7 @@ or sample.
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:func:`median_grouped` Median, or 50th percentile, of grouped data.
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:func:`mode` Single mode (most common value) of discrete or nominal data.
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:func:`multimode` List of modes (most common values) of discrete or nomimal data.
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:func:`quantiles` Divide data into intervals with equal probability.
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======================= ===============================================================
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Measures of spread
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@ -499,6 +500,53 @@ However, for reading convenience, most of the examples show sorted sequences.
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:func:`pvariance` function as the *mu* parameter to get the variance of a
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sample.
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.. function:: quantiles(dist, *, n=4, method='exclusive')
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Divide *dist* into *n* continuous intervals with equal probability.
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Returns a list of ``n - 1`` cut points separating the intervals.
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Set *n* to 4 for quartiles (the default). Set *n* to 10 for deciles. Set
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*n* to 100 for percentiles which gives the 99 cuts points that separate
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*dist* in to 100 equal sized groups. Raises :exc:`StatisticsError` if *n*
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is not least 1.
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The *dist* can be any iterable containing sample data or it can be an
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instance of a class that defines an :meth:`~inv_cdf` method.
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Raises :exc:`StatisticsError` if there are not at least two data points.
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For sample data, the cut points are linearly interpolated from the
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two nearest data points. For example, if a cut point falls one-third
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of the distance between two sample values, ``100`` and ``112``, the
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cut-point will evaluate to ``104``. Other selection methods may be
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offered in the future (for example choose ``100`` as the nearest
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value or compute ``106`` as the midpoint). This might matter if
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there are too few samples for a given number of cut points.
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If *method* is set to *inclusive*, *dist* is treated as population data.
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The minimum value is treated as the 0th percentile and the maximum
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value is treated as the 100th percentile. If *dist* is an instance of
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a class that defines an :meth:`~inv_cdf` method, setting *method*
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has no effect.
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.. doctest::
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# Decile cut points for empirically sampled data
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>>> data = [105, 129, 87, 86, 111, 111, 89, 81, 108, 92, 110,
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... 100, 75, 105, 103, 109, 76, 119, 99, 91, 103, 129,
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... 106, 101, 84, 111, 74, 87, 86, 103, 103, 106, 86,
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... 111, 75, 87, 102, 121, 111, 88, 89, 101, 106, 95,
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... 103, 107, 101, 81, 109, 104]
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>>> [round(q, 1) for q in quantiles(data, n=10)]
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[81.0, 86.2, 89.0, 99.4, 102.5, 103.6, 106.0, 109.8, 111.0]
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>>> # Quartile cut points for the standard normal distibution
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>>> Z = NormalDist()
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>>> [round(q, 4) for q in quantiles(Z, n=4)]
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[-0.6745, 0.0, 0.6745]
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.. versionadded:: 3.8
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Exceptions
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----------
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@ -606,7 +654,7 @@ of applications in statistics.
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<http://www.iceaaonline.com/ready/wp-content/uploads/2014/06/MM-9-Presentation-Meet-the-Overlapping-Coefficient-A-Measure-for-Elevator-Speeches.pdf>`_
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between two normal distributions, giving a measure of agreement.
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Returns a value between 0.0 and 1.0 giving `the overlapping area for
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two probability density functions
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the two probability density functions
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<https://www.rasch.org/rmt/rmt101r.htm>`_.
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Instances of :class:`NormalDist` support addition, subtraction,
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@ -649,8 +697,8 @@ of applications in statistics.
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For example, given `historical data for SAT exams
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<https://blog.prepscholar.com/sat-standard-deviation>`_ showing that scores
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are normally distributed with a mean of 1060 and a standard deviation of 192,
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determine the percentage of students with scores between 1100 and 1200, after
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rounding to the nearest whole number:
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determine the percentage of students with test scores between 1100 and
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1200, after rounding to the nearest whole number:
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.. doctest::
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@ -337,6 +337,10 @@ Added :func:`statistics.geometric_mean()`
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Added :func:`statistics.multimode` that returns a list of the most
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common values. (Contributed by Raymond Hettinger in :issue:`35892`.)
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Added :func:`statistics.quantiles` that divides data or a distribution
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in to equiprobable intervals (e.g. quartiles, deciles, or percentiles).
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(Contributed by Raymond Hettinger in :issue:`36546`.)
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Added :class:`statistics.NormalDist`, a tool for creating
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and manipulating normal distributions of a random variable.
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(Contributed by Raymond Hettinger in :issue:`36018`.)
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@ -7,9 +7,9 @@ averages, variance, and standard deviation.
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Calculating averages
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--------------------
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================== =============================================
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================== ==================================================
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Function Description
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================== =============================================
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================== ==================================================
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mean Arithmetic mean (average) of data.
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geometric_mean Geometric mean of data.
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harmonic_mean Harmonic mean of data.
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@ -19,7 +19,8 @@ median_high High median of data.
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median_grouped Median, or 50th percentile, of grouped data.
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mode Mode (most common value) of data.
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multimode List of modes (most common values of data).
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================== =============================================
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quantiles Divide data into intervals with equal probability.
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================== ==================================================
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Calculate the arithmetic mean ("the average") of data:
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@ -78,7 +79,7 @@ A single exception is defined: StatisticsError is a subclass of ValueError.
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"""
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__all__ = [ 'StatisticsError', 'NormalDist',
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__all__ = [ 'StatisticsError', 'NormalDist', 'quantiles',
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'pstdev', 'pvariance', 'stdev', 'variance',
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'median', 'median_low', 'median_high', 'median_grouped',
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'mean', 'mode', 'multimode', 'harmonic_mean', 'fmean',
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@ -562,6 +563,54 @@ def multimode(data):
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maxcount, mode_items = next(groupby(counts, key=itemgetter(1)), (0, []))
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return list(map(itemgetter(0), mode_items))
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def quantiles(dist, *, n=4, method='exclusive'):
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'''Divide *dist* into *n* continuous intervals with equal probability.
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Returns a list of (n - 1) cut points separating the intervals.
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Set *n* to 4 for quartiles (the default). Set *n* to 10 for deciles.
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Set *n* to 100 for percentiles which gives the 99 cuts points that
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separate *dist* in to 100 equal sized groups.
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The *dist* can be any iterable containing sample data or it can be
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an instance of a class that defines an inv_cdf() method. For sample
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data, the cut points are linearly interpolated between data points.
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If *method* is set to *inclusive*, *dist* is treated as population
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data. The minimum value is treated as the 0th percentile and the
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maximum value is treated as the 100th percentile.
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'''
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# Possible future API extensions:
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# quantiles(data, already_sorted=True)
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# quantiles(data, cut_points=[0.02, 0.25, 0.50, 0.75, 0.98])
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if n < 1:
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raise StatisticsError('n must be at least 1')
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if hasattr(dist, 'inv_cdf'):
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return [dist.inv_cdf(i / n) for i in range(1, n)]
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data = sorted(dist)
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ld = len(data)
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if ld < 2:
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raise StatisticsError('must have at least two data points')
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if method == 'inclusive':
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m = ld - 1
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result = []
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for i in range(1, n):
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j = i * m // n
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delta = i*m - j*n
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interpolated = (data[j] * (n - delta) + data[j+1] * delta) / n
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result.append(interpolated)
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return result
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if method == 'exclusive':
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m = ld + 1
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result = []
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for i in range(1, n):
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j = i * m // n # rescale i to m/n
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j = 1 if j < 1 else ld-1 if j > ld-1 else j # clamp to 1 .. ld-1
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delta = i*m - j*n # exact integer math
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interpolated = (data[j-1] * (n - delta) + data[j] * delta) / n
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result.append(interpolated)
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return result
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raise ValueError(f'Unknown method: {method!r}')
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# === Measures of spread ===
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@ -3,6 +3,7 @@ approx_equal function.
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"""
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import bisect
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import collections
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import collections.abc
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import copy
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@ -2038,6 +2039,7 @@ class TestStdev(VarianceStdevMixin, NumericTestCase):
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expected = math.sqrt(statistics.variance(data))
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self.assertEqual(self.func(data), expected)
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class TestGeometricMean(unittest.TestCase):
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def test_basics(self):
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@ -2126,6 +2128,146 @@ class TestGeometricMean(unittest.TestCase):
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with self.assertRaises(ValueError):
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geometric_mean([Inf, -Inf])
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class TestQuantiles(unittest.TestCase):
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def test_specific_cases(self):
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# Match results computed by hand and cross-checked
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# against the PERCENTILE.EXC function in MS Excel.
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quantiles = statistics.quantiles
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data = [120, 200, 250, 320, 350]
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random.shuffle(data)
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for n, expected in [
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(1, []),
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(2, [250.0]),
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(3, [200.0, 320.0]),
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(4, [160.0, 250.0, 335.0]),
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(5, [136.0, 220.0, 292.0, 344.0]),
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(6, [120.0, 200.0, 250.0, 320.0, 350.0]),
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(8, [100.0, 160.0, 212.5, 250.0, 302.5, 335.0, 357.5]),
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(10, [88.0, 136.0, 184.0, 220.0, 250.0, 292.0, 326.0, 344.0, 362.0]),
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(12, [80.0, 120.0, 160.0, 200.0, 225.0, 250.0, 285.0, 320.0, 335.0,
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350.0, 365.0]),
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(15, [72.0, 104.0, 136.0, 168.0, 200.0, 220.0, 240.0, 264.0, 292.0,
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320.0, 332.0, 344.0, 356.0, 368.0]),
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]:
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self.assertEqual(expected, quantiles(data, n=n))
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self.assertEqual(len(quantiles(data, n=n)), n - 1)
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self.assertEqual(list(map(float, expected)),
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quantiles(map(Decimal, data), n=n))
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self.assertEqual(list(map(Decimal, expected)),
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quantiles(map(Decimal, data), n=n))
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self.assertEqual(list(map(Fraction, expected)),
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quantiles(map(Fraction, data), n=n))
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# Invariant under tranlation and scaling
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def f(x):
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return 3.5 * x - 1234.675
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exp = list(map(f, expected))
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act = quantiles(map(f, data), n=n)
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self.assertTrue(all(math.isclose(e, a) for e, a in zip(exp, act)))
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# Quartiles of a standard normal distribution
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for n, expected in [
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(1, []),
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(2, [0.0]),
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(3, [-0.4307, 0.4307]),
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(4 ,[-0.6745, 0.0, 0.6745]),
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]:
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actual = quantiles(statistics.NormalDist(), n=n)
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self.assertTrue(all(math.isclose(e, a, abs_tol=0.0001)
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for e, a in zip(expected, actual)))
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def test_specific_cases_inclusive(self):
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# Match results computed by hand and cross-checked
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# against the PERCENTILE.INC function in MS Excel
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# and against the quaatile() function in SciPy.
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quantiles = statistics.quantiles
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data = [100, 200, 400, 800]
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random.shuffle(data)
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for n, expected in [
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(1, []),
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(2, [300.0]),
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(3, [200.0, 400.0]),
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(4, [175.0, 300.0, 500.0]),
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(5, [160.0, 240.0, 360.0, 560.0]),
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(6, [150.0, 200.0, 300.0, 400.0, 600.0]),
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(8, [137.5, 175, 225.0, 300.0, 375.0, 500.0,650.0]),
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(10, [130.0, 160.0, 190.0, 240.0, 300.0, 360.0, 440.0, 560.0, 680.0]),
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(12, [125.0, 150.0, 175.0, 200.0, 250.0, 300.0, 350.0, 400.0,
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500.0, 600.0, 700.0]),
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(15, [120.0, 140.0, 160.0, 180.0, 200.0, 240.0, 280.0, 320.0, 360.0,
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400.0, 480.0, 560.0, 640.0, 720.0]),
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]:
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self.assertEqual(expected, quantiles(data, n=n, method="inclusive"))
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self.assertEqual(len(quantiles(data, n=n, method="inclusive")), n - 1)
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self.assertEqual(list(map(float, expected)),
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quantiles(map(Decimal, data), n=n, method="inclusive"))
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self.assertEqual(list(map(Decimal, expected)),
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quantiles(map(Decimal, data), n=n, method="inclusive"))
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self.assertEqual(list(map(Fraction, expected)),
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quantiles(map(Fraction, data), n=n, method="inclusive"))
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# Invariant under tranlation and scaling
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def f(x):
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return 3.5 * x - 1234.675
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exp = list(map(f, expected))
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act = quantiles(map(f, data), n=n, method="inclusive")
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self.assertTrue(all(math.isclose(e, a) for e, a in zip(exp, act)))
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# Quartiles of a standard normal distribution
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for n, expected in [
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(1, []),
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(2, [0.0]),
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(3, [-0.4307, 0.4307]),
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(4 ,[-0.6745, 0.0, 0.6745]),
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]:
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actual = quantiles(statistics.NormalDist(), n=n, method="inclusive")
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self.assertTrue(all(math.isclose(e, a, abs_tol=0.0001)
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for e, a in zip(expected, actual)))
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def test_equal_sized_groups(self):
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quantiles = statistics.quantiles
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total = 10_000
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data = [random.expovariate(0.2) for i in range(total)]
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while len(set(data)) != total:
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data.append(random.expovariate(0.2))
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data.sort()
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# Cases where the group size exactly divides the total
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for n in (1, 2, 5, 10, 20, 50, 100, 200, 500, 1000, 2000, 5000, 10000):
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group_size = total // n
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self.assertEqual(
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[bisect.bisect(data, q) for q in quantiles(data, n=n)],
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list(range(group_size, total, group_size)))
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# When the group sizes can't be exactly equal, they should
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# differ by no more than one
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for n in (13, 19, 59, 109, 211, 571, 1019, 1907, 5261, 9769):
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group_sizes = {total // n, total // n + 1}
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pos = [bisect.bisect(data, q) for q in quantiles(data, n=n)]
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sizes = {q - p for p, q in zip(pos, pos[1:])}
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self.assertTrue(sizes <= group_sizes)
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def test_error_cases(self):
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quantiles = statistics.quantiles
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StatisticsError = statistics.StatisticsError
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with self.assertRaises(TypeError):
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quantiles() # Missing arguments
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with self.assertRaises(TypeError):
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quantiles([10, 20, 30], 13, n=4) # Too many arguments
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with self.assertRaises(TypeError):
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quantiles([10, 20, 30], 4) # n is a positional argument
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with self.assertRaises(StatisticsError):
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quantiles([10, 20, 30], n=0) # n is zero
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with self.assertRaises(StatisticsError):
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quantiles([10, 20, 30], n=-1) # n is negative
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with self.assertRaises(TypeError):
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quantiles([10, 20, 30], n=1.5) # n is not an integer
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with self.assertRaises(ValueError):
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quantiles([10, 20, 30], method='X') # method is unknown
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with self.assertRaises(StatisticsError):
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quantiles([10], n=4) # not enough data points
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with self.assertRaises(TypeError):
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quantiles([10, None, 30], n=4) # data is non-numeric
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class TestNormalDist(unittest.TestCase):
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# General note on precision: The pdf(), cdf(), and overlap() methods
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@ -0,0 +1 @@
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Add statistics.quantiles()
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