Method test_overlap

Lib/test/test_statistics.py:3115–3176

(self)

                            for e, a in zip(expected, actual)))

    def test_overlap(self):
        NormalDist = self.module.NormalDist

        # Match examples from Imman and Bradley
        for X1, X2, published_result in [
                (NormalDist(0.0, 2.0), NormalDist(1.0, 2.0), 0.80258),
                (NormalDist(0.0, 1.0), NormalDist(1.0, 2.0), 0.60993),
            ]:
            self.assertAlmostEqual(X1.overlap(X2), published_result, places=4)
            self.assertAlmostEqual(X2.overlap(X1), published_result, places=4)

        # Check against integration of the PDF
        def overlap_numeric(X, Y, *, steps=8_192, z=5):
            'Numerical integration cross-check for overlap() '
            fsum = math.fsum
            center = (X.mean + Y.mean) / 2.0
            width = z * max(X.stdev, Y.stdev)
            start = center - width
            dx = 2.0 * width / steps
            x_arr = [start + i*dx for i in range(steps)]
            xp = list(map(X.pdf, x_arr))
            yp = list(map(Y.pdf, x_arr))
            total = max(fsum(xp), fsum(yp))
            return fsum(map(min, xp, yp)) / total

        for X1, X2 in [
                # Examples from Imman and Bradley
                (NormalDist(0.0, 2.0), NormalDist(1.0, 2.0)),
                (NormalDist(0.0, 1.0), NormalDist(1.0, 2.0)),
                # Example from https://www.rasch.org/rmt/rmt101r.htm
                (NormalDist(0.0, 1.0), NormalDist(1.0, 2.0)),
                # Gender heights from http://www.usablestats.com/lessons/normal
                (NormalDist(70, 4), NormalDist(65, 3.5)),
                # Misc cases with equal standard deviations
                (NormalDist(100, 15), NormalDist(110, 15)),
                (NormalDist(-100, 15), NormalDist(110, 15)),
                (NormalDist(-100, 15), NormalDist(-110, 15)),
                # Misc cases with unequal standard deviations
                (NormalDist(100, 12), NormalDist(100, 15)),
                (NormalDist(100, 12), NormalDist(110, 15)),
                (NormalDist(100, 12), NormalDist(150, 15)),
                (NormalDist(100, 12), NormalDist(150, 35)),
                # Misc cases with small values
                (NormalDist(1.000, 0.002), NormalDist(1.001, 0.003)),
                (NormalDist(1.000, 0.002), NormalDist(1.006, 0.0003)),
                (NormalDist(1.000, 0.002), NormalDist(1.001, 0.099)),
            ]:
            self.assertAlmostEqual(X1.overlap(X2), overlap_numeric(X1, X2), places=5)
            self.assertAlmostEqual(X2.overlap(X1), overlap_numeric(X1, X2), places=5)

        # Error cases
        X = NormalDist()
        with self.assertRaises(TypeError):
            X.overlap()                             # too few arguments
        with self.assertRaises(TypeError):
            X.overlap(X, X)                         # too may arguments
        with self.assertRaises(TypeError):
            X.overlap(None)                         # right operand not a NormalDist