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Add overlap() method to statistics.NormalDist() #80350

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rhettinger opened this issue Mar 2, 2019 · 3 comments
Closed

Add overlap() method to statistics.NormalDist() #80350

rhettinger opened this issue Mar 2, 2019 · 3 comments
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3.8 only security fixes stdlib Python modules in the Lib dir

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@rhettinger
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BPO 36169
Nosy @tim-one, @rhettinger, @mdickinson, @stevendaprano, @applio
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  • bpo-36169 : Add overlap() method to statistics.NormalDist #12149
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    Note: these values reflect the state of the issue at the time it was migrated and might not reflect the current state.

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    GitHub fields:

    assignee = None
closed_at = <Date 2019-03-07.07:00:03.569>
created_at = <Date 2019-03-02.23:04:32.531>
labels = ['3.8', 'library']
title = 'Add overlap() method to statistics.NormalDist()'
updated_at = <Date 2019-03-07.07:00:03.568>
user = 'https://github.com/rhettinger'

    bugs.python.org fields:

    activity = <Date 2019-03-07.07:00:03.568>
actor = 'rhettinger'
assignee = 'none'
closed = True
closed_date = <Date 2019-03-07.07:00:03.569>
closer = 'rhettinger'
components = ['Library (Lib)']
creation = <Date 2019-03-02.23:04:32.531>
creator = 'rhettinger'
dependencies = []
files = []
hgrepos = []
issue_num = 36169
keywords = ['patch']
message_count = 3.0
messages = ['337020', '337026', '337367']
nosy_count = 5.0
nosy_names = ['tim.peters', 'rhettinger', 'mark.dickinson', 'steven.daprano', 'davin']
pr_nums = ['12149']
priority = 'normal'
resolution = 'fixed'
stage = 'resolved'
status = 'closed'
superseder = None
type = None
url = 'https://bugs.python.org/issue36169'
versions = ['Python 3.8']
    @rhettinger
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    ------ How to use it ------

    What percentage of men and women will have the same height in two normally distributed populations with known means and standard deviations?

        # http://www.usablestats.com/lessons/normal
    >>> men = NormalDist(70, 4)
    >>> women = NormalDist(65, 3.5)
    >>> men.overlap(women)
    0.5028719270195425

    The result can be confirmed empirically with a Monte Carlo simulation:

        >>> from collections import Counter
    >>> n = 100_000
    >>> overlap = Counter(map(round, men.samples(n))) & Counter(map(round, women.samples(n)))
    >>> sum(overlap.values()) / n
    0.50349

    The result can also be confirmed by numeric integration of the probability density function:

        >>> dx = 0.10
    >>> heights = [h * dx for h in range(500, 860)]
    >>> sum(min(men.pdf(h), women.pdf(h)) for h in heights) * dx
    0.5028920586287203

    ------ Code ------

        def overlap(self, other):
        '''Compute the overlap coefficient (OVL) between two normal distributions.
        Measures the agreement between two normal probability distributions.
    Returns a value between 0.0 and 1.0 giving the overlapping area in
    the two underlying probability density functions.

    '''

    # See: "The overlapping coefficient as a measure of agreement between
    # probability distributions and point estimation of the overlap of two
    # normal densities" -- Henry F. Inman and Edwin L. Bradley Jr
    # http://dx.doi.org/10.1080/03610928908830127

    # Also see:
    # http://www.iceaaonline.com/ready/wp-content/uploads/2014/06/MM-9-Presentation-Meet-the-Overlapping-Coefficient-A-Measure-for-Elevator-Speeches.pdf

            if not isinstance(other, NormalDist):
            return NotImplemented
        X, Y = self, other
        X_var, Y_var = X.variance, Y.variance
        if not X_var or not Y_var:
            raise StatisticsError('overlap() not defined when sigma is zero')
        dv = Y_var - X_var
        if not dv:
            return 2.0 * NormalDist(fabs(Y.mu - X.mu), 2.0 * X.sigma).cdf(0)
        a = X.mu * Y_var - Y.mu * X_var
        b = X.sigma * Y.sigma * sqrt((X.mu - Y.mu)**2 + dv * log(Y_var / X_var))
        x1 = (a + b) / dv
        x2 = (a - b) / dv
        return 1.0 - (fabs(Y.cdf(x1) - X.cdf(x1)) + fabs(Y.cdf(x2) - X.cdf(x2)))

    ---- Future ----

    The concept of an overlap coefficient (OVL) is not specific to normal distributions, so it is possible to extend this idea to work with other distributions if needed.

    @rhettinger rhettinger added 3.8 only security fixes stdlib Python modules in the Lib dir labels Mar 2, 2019
    @rhettinger
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    Another cross-check can be had with this nomogram: https://www.rasch.org/rmt/rmt101r.htm

    @rhettinger
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    New changeset 318d537 by Raymond Hettinger in branch 'master':
    bpo-36169 : Add overlap() method to statistics.NormalDist (GH-12149)
    318d537

    @ezio-melotti ezio-melotti transferred this issue from another repository Apr 10, 2022
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