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diff --git a/Doc/library/statistics.rst b/Doc/library/statistics.rst index 8f8c009..be0215a 100644 --- a/Doc/library/statistics.rst +++ b/Doc/library/statistics.rst @@ -549,6 +549,28 @@ of applications in statistics, including simulations and hypothesis testing. compute the probability that a random variable *X* will be less than or equal to *x*. Mathematically, it is written ``P(X <= x)``. + .. method:: NormalDist.overlap(other) + + Compute the `overlapping coefficient (OVL) + <http://www.iceaaonline.com/ready/wp-content/uploads/2014/06/MM-9-Presentation-Meet-the-Overlapping-Coefficient-A-Measure-for-Elevator-Speeches.pdf>`_ + 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 for + two probability density functions. + + In this `example from John M. Linacre + <https://www.rasch.org/rmt/rmt101r.htm>`_ about 80% of each + distribution overlaps the other: + + .. doctest:: + + >>> N1 = NormalDist(2.4, 1.6) + >>> N2 = NormalDist(3.2, 2.0) + >>> ovl = N1.overlap(N2) + >>> f'{ovl * 100.0 :.1f}%' + '80.4%' + Instances of :class:`NormalDist` support addition, subtraction, multiplication and division by a constant. These operations are used for translation and scaling. For example: @@ -595,6 +617,16 @@ determine the percentage of students with scores between 1100 and 1200: >>> f'{fraction * 100 :.1f}% score between 1100 and 1200' '18.2% score between 1100 and 1200' +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) + >>> ovl = men.overlap(women) + >>> round(ovl * 100.0, 1) + 50.3 + To estimate the distribution for a model than isn't easy to solve analytically, :class:`NormalDist` can generate input samples for a `Monte Carlo simulation <https://en.wikipedia.org/wiki/Monte_Carlo_method>`_ of the |