Method test_kde

Lib/test/test_statistics.py:2357–2434

(self)

    @support.requires_resource('cpu')
    def test_kde(self):
        kde = statistics.kde
        StatisticsError = statistics.StatisticsError

        kernels = ['normal', 'gauss', 'logistic', 'sigmoid', 'rectangular',
                   'uniform', 'triangular', 'parabolic', 'epanechnikov',
                   'quartic', 'biweight', 'triweight', 'cosine']

        sample = [-2.1, -1.3, -0.4, 1.9, 5.1, 6.2]

        # The approximate integral of a PDF should be close to 1.0

        def integrate(func, low, high, steps=10_000):
            "Numeric approximation of a definite function integral."
            dx = (high - low) / steps
            midpoints = (low + (i + 1/2) * dx for i in range(steps))
            return sum(map(func, midpoints)) * dx

        for kernel in kernels:
            with self.subTest(kernel=kernel):
                f_hat = kde(sample, h=1.5, kernel=kernel)
                area = integrate(f_hat, -20, 20)
                self.assertAlmostEqual(area, 1.0, places=4)

        # Check CDF against an integral of the PDF

        data = [3, 5, 10, 12]
        h = 2.3
        x = 10.5
        for kernel in kernels:
            with self.subTest(kernel=kernel):
                cdf = kde(data, h, kernel, cumulative=True)
                f_hat = kde(data, h, kernel)
                area = integrate(f_hat, -20, x, 100_000)
                self.assertAlmostEqual(cdf(x), area, places=4)

        # Check error cases

        with self.assertRaises(StatisticsError):
            kde([], h=1.0)                              # Empty dataset
        with self.assertRaises(TypeError):
            kde(['abc', 'def'], 1.5)                    # Non-numeric data
        with self.assertRaises(TypeError):
            kde(iter(sample), 1.5)                      # Data is not a sequence
        with self.assertRaises(StatisticsError):
            kde(sample, h=0.0)                          # Zero bandwidth
        with self.assertRaises(StatisticsError):
            kde(sample, h=-1.0)                         # Negative bandwidth
        with self.assertRaises(TypeError):
            kde(sample, h='str')                        # Wrong bandwidth type
        with self.assertRaises(StatisticsError):
            kde(sample, h=1.0, kernel='bogus')          # Invalid kernel
        with self.assertRaises(TypeError):
            kde(sample, 1.0, 'gauss', True)             # Positional cumulative argument

        # Test name and docstring of the generated function

        h = 1.5