[3.8] bpo-36324: Apply review comments from Allen Downey (GH-15693) by miss-islington · Pull Request #15694 · python/cpython
Expand Up
@@ -26,10 +26,10 @@ numeric (:class:`Real`-valued) data.
Unless explicitly noted otherwise, these functions support :class:`int`,
:class:`float`, :class:`decimal.Decimal` and :class:`fractions.Fraction`.
Behaviour with other types (whether in the numeric tower or not) is
currently unsupported. Mixed types are also undefined and
implementation-dependent. If your input data consists of mixed types,
you may be able to use :func:`map` to ensure a consistent result, e.g.
``map(float, input_data)``.
currently unsupported. Collections with a mix of types are also undefined
and implementation-dependent. If your input data consists of mixed types,
you may be able to use :func:`map` to ensure a consistent result, for
example: ``map(float, input_data)``.
Averages and measures of central location ----------------------------------------- Expand Down Expand Up @@ -102,11 +102,9 @@ However, for reading convenience, most of the examples show sorted sequences. .. note::
The mean is strongly affected by outliers and is not a robust estimator for central location: the mean is not necessarily a typical example of the data points. For more robust, although less efficient, measures of central location, see :func:`median` and :func:`mode`. (In this case, "efficient" refers to statistical efficiency rather than computational efficiency.) for central location: the mean is not necessarily a typical example of the data points. For more robust measures of central location, see :func:`median` and :func:`mode`.
The sample mean gives an unbiased estimate of the true population mean, which means that, taken on average over all the possible samples, Expand All @@ -120,9 +118,8 @@ However, for reading convenience, most of the examples show sorted sequences. Convert *data* to floats and compute the arithmetic mean.
This runs faster than the :func:`mean` function and it always returns a :class:`float`. The result is highly accurate but not as perfect as :func:`mean`. If the input dataset is empty, raises a :exc:`StatisticsError`. :class:`float`. The *data* may be a sequence or iterator. If the input dataset is empty, raises a :exc:`StatisticsError`.
.. doctest::
Expand All @@ -136,15 +133,20 @@ However, for reading convenience, most of the examples show sorted sequences.
Convert *data* to floats and compute the geometric mean.
The geometric mean indicates the central tendency or typical value of the *data* using the product of the values (as opposed to the arithmetic mean which uses their sum).
Raises a :exc:`StatisticsError` if the input dataset is empty, if it contains a zero, or if it contains a negative value. The *data* may be a sequence or iterator.
No special efforts are made to achieve exact results. (However, this may change in the future.)
.. doctest::
>>> round(geometric_mean([54, 24, 36]), 9) >>> round(geometric_mean([54, 24, 36]), 1) 36.0
.. versionadded:: 3.8 Expand Down Expand Up @@ -174,7 +176,7 @@ However, for reading convenience, most of the examples show sorted sequences. 3.6
Using the arithmetic mean would give an average of about 5.167, which is too high. is well over the aggregate P/E ratio.
:exc:`StatisticsError` is raised if *data* is empty, or any element is less than zero. Expand Down Expand Up @@ -312,10 +314,10 @@ However, for reading convenience, most of the examples show sorted sequences. The mode (when it exists) is the most typical value and serves as a measure of central location.
If there are multiple modes, returns the first one encountered in the *data*. If the smallest or largest of multiple modes is desired instead, use ``min(multimode(data))`` or ``max(multimode(data))``. If the input *data* is empty, :exc:`StatisticsError` is raised. If there are multiple modes with the same frequency, returns the first one encountered in the *data*. If the smallest or largest of those is desired instead, use ``min(multimode(data))`` or ``max(multimode(data))``. If the input *data* is empty, :exc:`StatisticsError` is raised.
``mode`` assumes discrete data, and returns a single value. This is the standard treatment of the mode as commonly taught in schools: Expand All @@ -325,8 +327,8 @@ However, for reading convenience, most of the examples show sorted sequences. >>> mode([1, 1, 2, 3, 3, 3, 3, 4]) 3
The mode is unique in that it is the only statistic which also applies to nominal (non-numeric) data: The mode is unique in that it is the only statistic in this package that also applies to nominal (non-numeric) data:
.. doctest::
Expand Down Expand Up @@ -368,15 +370,16 @@ However, for reading convenience, most of the examples show sorted sequences.
.. function:: pvariance(data, mu=None)
Return the population variance of *data*, a non-empty iterable of real-valued numbers. Variance, or second moment about the mean, is a measure of the variability (spread or dispersion) of data. A large variance indicates that the data is spread out; a small variance indicates it is clustered closely around the mean. Return the population variance of *data*, a non-empty sequence or iterator of real-valued numbers. Variance, or second moment about the mean, is a measure of the variability (spread or dispersion) of data. A large variance indicates that the data is spread out; a small variance indicates it is clustered closely around the mean.
If the optional second argument *mu* is given, it should be the mean of *data*. If it is missing or ``None`` (the default), the mean is automatically calculated. If the optional second argument *mu* is given, it is typically the mean of the *data*. It can also be used to compute the second moment around a point that is not the mean. If it is missing or ``None`` (the default), the arithmetic mean is automatically calculated.
Use this function to calculate the variance from the entire population. To estimate the variance from a sample, the :func:`variance` function is usually Expand All @@ -401,10 +404,6 @@ However, for reading convenience, most of the examples show sorted sequences. >>> pvariance(data, mu) 1.25
This function does not attempt to verify that you have passed the actual mean as *mu*. Using arbitrary values for *mu* may lead to invalid or impossible results.
Decimals and Fractions are supported:
.. doctest:: Expand All @@ -423,11 +422,11 @@ However, for reading convenience, most of the examples show sorted sequences. σ². When called on a sample instead, this is the biased sample variance s², also known as variance with N degrees of freedom.
If you somehow know the true population mean μ, you may use this function to calculate the variance of a sample, giving the known population mean as the second argument. Provided the data points are representative (e.g. independent and identically distributed), the result will be an unbiased estimate of the population variance. If you somehow know the true population mean μ, you may use this function to calculate the variance of a sample, giving the known population mean as the second argument. Provided the data points are a random sample of the population, the result will be an unbiased estimate of the population variance.
.. function:: stdev(data, xbar=None) Expand Down Expand Up @@ -502,19 +501,19 @@ However, for reading convenience, most of the examples show sorted sequences. :func:`pvariance` function as the *mu* parameter to get the variance of a sample.
.. function:: quantiles(dist, *, n=4, method='exclusive') .. function:: quantiles(data, *, n=4, method='exclusive')
Divide *dist* into *n* continuous intervals with equal probability. Divide *data* into *n* continuous intervals with equal probability. Returns a list of ``n - 1`` cut points separating the intervals.
Set *n* to 4 for quartiles (the default). Set *n* to 10 for deciles. Set *n* to 100 for percentiles which gives the 99 cuts points that separate *dist* in to 100 equal sized groups. Raises :exc:`StatisticsError` if *n* *data* in to 100 equal sized groups. Raises :exc:`StatisticsError` if *n* is not least 1.
The *dist* can be any iterable containing sample data or it can be an The *data* can be any iterable containing sample data or it can be an instance of a class that defines an :meth:`~inv_cdf` method. For meaningful results, the number of data points in *dist* should be larger than *n*. results, the number of data points in *data* should be larger than *n*. Raises :exc:`StatisticsError` if there are not at least two data points.
For sample data, the cut points are linearly interpolated from the Expand All @@ -523,7 +522,7 @@ However, for reading convenience, most of the examples show sorted sequences. cut-point will evaluate to ``104``.
The *method* for computing quantiles can be varied depending on whether the data in *dist* includes or excludes the lowest and whether the data in *data* includes or excludes the lowest and highest possible values from the population.
The default *method* is "exclusive" and is used for data sampled from Expand All @@ -535,14 +534,14 @@ However, for reading convenience, most of the examples show sorted sequences.
Setting the *method* to "inclusive" is used for describing population data or for samples that are known to include the most extreme values from the population. The minimum value in *dist* is treated as the 0th from the population. The minimum value in *data* is treated as the 0th percentile and the maximum value is treated as the 100th percentile. The portion of the population falling below the *i-th* of *m* sorted data points is computed as ``(i - 1) / (m - 1)``. Given 11 sample values, the method sorts them and assigns the following percentiles: 0%, 10%, 20%, 30%, 40%, 50%, 60%, 70%, 80%, 90%, 100%.
If *dist* is an instance of a class that defines an If *data* is an instance of a class that defines an :meth:`~inv_cdf` method, setting *method* has no effect.
.. doctest:: Expand Down Expand Up @@ -580,7 +579,7 @@ A single exception is defined: :class:`NormalDist` is a tool for creating and manipulating normal distributions of a `random variable <http://www.stat.yale.edu/Courses/1997-98/101/ranvar.htm>`_. It is a composite class that treats the mean and standard deviation of data class that treats the mean and standard deviation of data measurements as a single entity.
Normal distributions arise from the `Central Limit Theorem Expand Down Expand Up @@ -616,13 +615,14 @@ of applications in statistics.
.. classmethod:: NormalDist.from_samples(data)
Makes a normal distribution instance computed from sample data. The *data* can be any :term:`iterable` and should consist of values that can be converted to type :class:`float`. Makes a normal distribution instance with *mu* and *sigma* parameters estimated from the *data* using :func:`fmean` and :func:`stdev`.
If *data* does not contain at least two elements, raises :exc:`StatisticsError` because it takes at least one point to estimate a central value and at least two points to estimate dispersion. The *data* can be any :term:`iterable` and should consist of values that can be converted to type :class:`float`. If *data* does not contain at least two elements, raises :exc:`StatisticsError` because it takes at least one point to estimate a central value and at least two points to estimate dispersion.
.. method:: NormalDist.samples(n, *, seed=None)
Expand All @@ -636,10 +636,10 @@ of applications in statistics. .. method:: NormalDist.pdf(x)
Using a `probability density function (pdf) <https://en.wikipedia.org/wiki/Probability_density_function>`_, compute the relative likelihood that a random variable *X* will be near the given value *x*. Mathematically, it is the ratio ``P(x <= X < x+dx) / dx``. <https://en.wikipedia.org/wiki/Probability_density_function>`_, compute the relative likelihood that a random variable *X* will be near the given value *x*. Mathematically, it is the limit of the ratio ``P(x <= X < x+dx) / dx`` as *dx* approaches zero.
The relative likelihood is computed as the probability of a sample occurring in a narrow range divided by the width of the range (hence Expand Down Expand Up @@ -667,8 +667,10 @@ of applications in statistics.
.. method:: NormalDist.overlap(other)
Returns a value between 0.0 and 1.0 giving the overlapping area for the two probability density functions. Measures the agreement between two normal probability distributions. Returns a value between 0.0 and 1.0 giving `the overlapping area for the two probability density functions <https://www.rasch.org/rmt/rmt101r.htm>`_.
Instances of :class:`NormalDist` support addition, subtraction, multiplication and division by a constant. These operations Expand Down Expand Up @@ -740,12 +742,11 @@ Carlo simulation <https://en.wikipedia.org/wiki/Monte_Carlo_method>`_: ... return (3*x + 7*x*y - 5*y) / (11 * z) ... >>> n = 100_000 >>> seed = 86753099035768 >>> X = NormalDist(10, 2.5).samples(n, seed=seed) >>> Y = NormalDist(15, 1.75).samples(n, seed=seed) >>> Z = NormalDist(50, 1.25).samples(n, seed=seed) >>> NormalDist.from_samples(map(model, X, Y, Z)) # doctest: +SKIP NormalDist(mu=1.8661894803304777, sigma=0.65238717376862) >>> X = NormalDist(10, 2.5).samples(n, seed=3652260728) >>> Y = NormalDist(15, 1.75).samples(n, seed=4582495471) >>> Z = NormalDist(50, 1.25).samples(n, seed=6582483453) >>> quantiles(map(model, X, Y, Z)) # doctest: +SKIP [1.4591308524824727, 1.8035946855390597, 2.175091447274739]
Normal distributions commonly arise in machine learning problems.
Expand Down
Averages and measures of central location ----------------------------------------- Expand Down Expand Up @@ -102,11 +102,9 @@ However, for reading convenience, most of the examples show sorted sequences. .. note::
The mean is strongly affected by outliers and is not a robust estimator for central location: the mean is not necessarily a typical example of the data points. For more robust, although less efficient, measures of central location, see :func:`median` and :func:`mode`. (In this case, "efficient" refers to statistical efficiency rather than computational efficiency.) for central location: the mean is not necessarily a typical example of the data points. For more robust measures of central location, see :func:`median` and :func:`mode`.
The sample mean gives an unbiased estimate of the true population mean, which means that, taken on average over all the possible samples, Expand All @@ -120,9 +118,8 @@ However, for reading convenience, most of the examples show sorted sequences. Convert *data* to floats and compute the arithmetic mean.
This runs faster than the :func:`mean` function and it always returns a :class:`float`. The result is highly accurate but not as perfect as :func:`mean`. If the input dataset is empty, raises a :exc:`StatisticsError`. :class:`float`. The *data* may be a sequence or iterator. If the input dataset is empty, raises a :exc:`StatisticsError`.
.. doctest::
Expand All @@ -136,15 +133,20 @@ However, for reading convenience, most of the examples show sorted sequences.
Convert *data* to floats and compute the geometric mean.
The geometric mean indicates the central tendency or typical value of the *data* using the product of the values (as opposed to the arithmetic mean which uses their sum).
Raises a :exc:`StatisticsError` if the input dataset is empty, if it contains a zero, or if it contains a negative value. The *data* may be a sequence or iterator.
No special efforts are made to achieve exact results. (However, this may change in the future.)
.. doctest::
>>> round(geometric_mean([54, 24, 36]), 9) >>> round(geometric_mean([54, 24, 36]), 1) 36.0
.. versionadded:: 3.8 Expand Down Expand Up @@ -174,7 +176,7 @@ However, for reading convenience, most of the examples show sorted sequences. 3.6
Using the arithmetic mean would give an average of about 5.167, which is too high. is well over the aggregate P/E ratio.
:exc:`StatisticsError` is raised if *data* is empty, or any element is less than zero. Expand Down Expand Up @@ -312,10 +314,10 @@ However, for reading convenience, most of the examples show sorted sequences. The mode (when it exists) is the most typical value and serves as a measure of central location.
If there are multiple modes, returns the first one encountered in the *data*. If the smallest or largest of multiple modes is desired instead, use ``min(multimode(data))`` or ``max(multimode(data))``. If the input *data* is empty, :exc:`StatisticsError` is raised. If there are multiple modes with the same frequency, returns the first one encountered in the *data*. If the smallest or largest of those is desired instead, use ``min(multimode(data))`` or ``max(multimode(data))``. If the input *data* is empty, :exc:`StatisticsError` is raised.
``mode`` assumes discrete data, and returns a single value. This is the standard treatment of the mode as commonly taught in schools: Expand All @@ -325,8 +327,8 @@ However, for reading convenience, most of the examples show sorted sequences. >>> mode([1, 1, 2, 3, 3, 3, 3, 4]) 3
The mode is unique in that it is the only statistic which also applies to nominal (non-numeric) data: The mode is unique in that it is the only statistic in this package that also applies to nominal (non-numeric) data:
.. doctest::
Expand Down Expand Up @@ -368,15 +370,16 @@ However, for reading convenience, most of the examples show sorted sequences.
.. function:: pvariance(data, mu=None)
Return the population variance of *data*, a non-empty iterable of real-valued numbers. Variance, or second moment about the mean, is a measure of the variability (spread or dispersion) of data. A large variance indicates that the data is spread out; a small variance indicates it is clustered closely around the mean. Return the population variance of *data*, a non-empty sequence or iterator of real-valued numbers. Variance, or second moment about the mean, is a measure of the variability (spread or dispersion) of data. A large variance indicates that the data is spread out; a small variance indicates it is clustered closely around the mean.
If the optional second argument *mu* is given, it should be the mean of *data*. If it is missing or ``None`` (the default), the mean is automatically calculated. If the optional second argument *mu* is given, it is typically the mean of the *data*. It can also be used to compute the second moment around a point that is not the mean. If it is missing or ``None`` (the default), the arithmetic mean is automatically calculated.
Use this function to calculate the variance from the entire population. To estimate the variance from a sample, the :func:`variance` function is usually Expand All @@ -401,10 +404,6 @@ However, for reading convenience, most of the examples show sorted sequences. >>> pvariance(data, mu) 1.25
This function does not attempt to verify that you have passed the actual mean as *mu*. Using arbitrary values for *mu* may lead to invalid or impossible results.
Decimals and Fractions are supported:
.. doctest:: Expand All @@ -423,11 +422,11 @@ However, for reading convenience, most of the examples show sorted sequences. σ². When called on a sample instead, this is the biased sample variance s², also known as variance with N degrees of freedom.
If you somehow know the true population mean μ, you may use this function to calculate the variance of a sample, giving the known population mean as the second argument. Provided the data points are representative (e.g. independent and identically distributed), the result will be an unbiased estimate of the population variance. If you somehow know the true population mean μ, you may use this function to calculate the variance of a sample, giving the known population mean as the second argument. Provided the data points are a random sample of the population, the result will be an unbiased estimate of the population variance.
.. function:: stdev(data, xbar=None) Expand Down Expand Up @@ -502,19 +501,19 @@ However, for reading convenience, most of the examples show sorted sequences. :func:`pvariance` function as the *mu* parameter to get the variance of a sample.
.. function:: quantiles(dist, *, n=4, method='exclusive') .. function:: quantiles(data, *, n=4, method='exclusive')
Divide *dist* into *n* continuous intervals with equal probability. Divide *data* into *n* continuous intervals with equal probability. Returns a list of ``n - 1`` cut points separating the intervals.
Set *n* to 4 for quartiles (the default). Set *n* to 10 for deciles. Set *n* to 100 for percentiles which gives the 99 cuts points that separate *dist* in to 100 equal sized groups. Raises :exc:`StatisticsError` if *n* *data* in to 100 equal sized groups. Raises :exc:`StatisticsError` if *n* is not least 1.
The *dist* can be any iterable containing sample data or it can be an The *data* can be any iterable containing sample data or it can be an instance of a class that defines an :meth:`~inv_cdf` method. For meaningful results, the number of data points in *dist* should be larger than *n*. results, the number of data points in *data* should be larger than *n*. Raises :exc:`StatisticsError` if there are not at least two data points.
For sample data, the cut points are linearly interpolated from the Expand All @@ -523,7 +522,7 @@ However, for reading convenience, most of the examples show sorted sequences. cut-point will evaluate to ``104``.
The *method* for computing quantiles can be varied depending on whether the data in *dist* includes or excludes the lowest and whether the data in *data* includes or excludes the lowest and highest possible values from the population.
The default *method* is "exclusive" and is used for data sampled from Expand All @@ -535,14 +534,14 @@ However, for reading convenience, most of the examples show sorted sequences.
Setting the *method* to "inclusive" is used for describing population data or for samples that are known to include the most extreme values from the population. The minimum value in *dist* is treated as the 0th from the population. The minimum value in *data* is treated as the 0th percentile and the maximum value is treated as the 100th percentile. The portion of the population falling below the *i-th* of *m* sorted data points is computed as ``(i - 1) / (m - 1)``. Given 11 sample values, the method sorts them and assigns the following percentiles: 0%, 10%, 20%, 30%, 40%, 50%, 60%, 70%, 80%, 90%, 100%.
If *dist* is an instance of a class that defines an If *data* is an instance of a class that defines an :meth:`~inv_cdf` method, setting *method* has no effect.
.. doctest:: Expand Down Expand Up @@ -580,7 +579,7 @@ A single exception is defined: :class:`NormalDist` is a tool for creating and manipulating normal distributions of a `random variable <http://www.stat.yale.edu/Courses/1997-98/101/ranvar.htm>`_. It is a composite class that treats the mean and standard deviation of data class that treats the mean and standard deviation of data measurements as a single entity.
Normal distributions arise from the `Central Limit Theorem Expand Down Expand Up @@ -616,13 +615,14 @@ of applications in statistics.
.. classmethod:: NormalDist.from_samples(data)
Makes a normal distribution instance computed from sample data. The *data* can be any :term:`iterable` and should consist of values that can be converted to type :class:`float`. Makes a normal distribution instance with *mu* and *sigma* parameters estimated from the *data* using :func:`fmean` and :func:`stdev`.
If *data* does not contain at least two elements, raises :exc:`StatisticsError` because it takes at least one point to estimate a central value and at least two points to estimate dispersion. The *data* can be any :term:`iterable` and should consist of values that can be converted to type :class:`float`. If *data* does not contain at least two elements, raises :exc:`StatisticsError` because it takes at least one point to estimate a central value and at least two points to estimate dispersion.
.. method:: NormalDist.samples(n, *, seed=None)
Expand All @@ -636,10 +636,10 @@ of applications in statistics. .. method:: NormalDist.pdf(x)
Using a `probability density function (pdf) <https://en.wikipedia.org/wiki/Probability_density_function>`_, compute the relative likelihood that a random variable *X* will be near the given value *x*. Mathematically, it is the ratio ``P(x <= X < x+dx) / dx``. <https://en.wikipedia.org/wiki/Probability_density_function>`_, compute the relative likelihood that a random variable *X* will be near the given value *x*. Mathematically, it is the limit of the ratio ``P(x <= X < x+dx) / dx`` as *dx* approaches zero.
The relative likelihood is computed as the probability of a sample occurring in a narrow range divided by the width of the range (hence Expand Down Expand Up @@ -667,8 +667,10 @@ of applications in statistics.
.. method:: NormalDist.overlap(other)
Returns a value between 0.0 and 1.0 giving the overlapping area for the two probability density functions. Measures the agreement between two normal probability distributions. Returns a value between 0.0 and 1.0 giving `the overlapping area for the two probability density functions <https://www.rasch.org/rmt/rmt101r.htm>`_.
Instances of :class:`NormalDist` support addition, subtraction, multiplication and division by a constant. These operations Expand Down Expand Up @@ -740,12 +742,11 @@ Carlo simulation <https://en.wikipedia.org/wiki/Monte_Carlo_method>`_: ... return (3*x + 7*x*y - 5*y) / (11 * z) ... >>> n = 100_000 >>> seed = 86753099035768 >>> X = NormalDist(10, 2.5).samples(n, seed=seed) >>> Y = NormalDist(15, 1.75).samples(n, seed=seed) >>> Z = NormalDist(50, 1.25).samples(n, seed=seed) >>> NormalDist.from_samples(map(model, X, Y, Z)) # doctest: +SKIP NormalDist(mu=1.8661894803304777, sigma=0.65238717376862) >>> X = NormalDist(10, 2.5).samples(n, seed=3652260728) >>> Y = NormalDist(15, 1.75).samples(n, seed=4582495471) >>> Z = NormalDist(50, 1.25).samples(n, seed=6582483453) >>> quantiles(map(model, X, Y, Z)) # doctest: +SKIP [1.4591308524824727, 1.8035946855390597, 2.175091447274739]
Normal distributions commonly arise in machine learning problems.
Expand Down