Method test_inv_cdf

Lib/test/test_statistics.py:3035–3098

(self)

    @support.skip_if_pgo_task
    @support.requires_resource('cpu')
    def test_inv_cdf(self):
        NormalDist = self.module.NormalDist

        # Center case should be exact.
        iq = NormalDist(100, 15)
        self.assertEqual(iq.inv_cdf(0.50), iq.mean)

        # Test versus a published table of known percentage points.
        # See the second table at the bottom of the page here:
        # http://people.bath.ac.uk/masss/tables/normaltable.pdf
        Z = NormalDist()
        pp = {5.0: (0.000, 1.645, 2.576, 3.291, 3.891,
                    4.417, 4.892, 5.327, 5.731, 6.109),
              2.5: (0.674, 1.960, 2.807, 3.481, 4.056,
                    4.565, 5.026, 5.451, 5.847, 6.219),
              1.0: (1.282, 2.326, 3.090, 3.719, 4.265,
                    4.753, 5.199, 5.612, 5.998, 6.361)}
        for base, row in pp.items():
            for exp, x in enumerate(row, start=1):
                p = base * 10.0 ** (-exp)
                self.assertAlmostEqual(-Z.inv_cdf(p), x, places=3)
                p = 1.0 - p
                self.assertAlmostEqual(Z.inv_cdf(p), x, places=3)

        # Match published example for MS Excel
        # https://support.office.com/en-us/article/norm-inv-function-54b30935-fee7-493c-bedb-2278a9db7e13
        self.assertAlmostEqual(NormalDist(40, 1.5).inv_cdf(0.908789), 42.000002)

        # One million equally spaced probabilities
        n = 2**20
        for p in range(1, n):
            p /= n
            self.assertAlmostEqual(iq.cdf(iq.inv_cdf(p)), p)

        # One hundred ever smaller probabilities to test tails out to
        # extreme probabilities: 1 / 2**50 and (2**50-1) / 2 ** 50
        for e in range(1, 51):
            p = 2.0 ** (-e)
            self.assertAlmostEqual(iq.cdf(iq.inv_cdf(p)), p)
            p = 1.0 - p
            self.assertAlmostEqual(iq.cdf(iq.inv_cdf(p)), p)

        # Now apply cdf() first.  Near the tails, the round-trip loses
        # precision and is ill-conditioned (small changes in the inputs
        # give large changes in the output), so only check to 5 places.
        for x in range(200):
            self.assertAlmostEqual(iq.inv_cdf(iq.cdf(x)), x, places=5)

        # Error cases:
        with self.assertRaises(self.module.StatisticsError):
            iq.inv_cdf(0.0)                         # p is zero
        with self.assertRaises(self.module.StatisticsError):
            iq.inv_cdf(-0.1)                        # p under zero
        with self.assertRaises(self.module.StatisticsError):
            iq.inv_cdf(1.0)                         # p is one
        with self.assertRaises(self.module.StatisticsError):
            iq.inv_cdf(1.1)                         # p over one