------ 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)    0.5028719270195425The 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    0.50349The 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.

Another cross-check can be had with this nomogram:https://www.rasch.org/rmt/rmt101r.htm

New changeset318d537daabf2bd5f781255c7e25bfce260cf227 by Raymond Hettinger in branch 'master':bpo-36169 : Add overlap() method to statistics.NormalDist (GH-12149)https://github.com/python/cpython/commit/318d537daabf2bd5f781255c7e25bfce260cf227