179 lines
5.4 KiB
Python
179 lines
5.4 KiB
Python
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"""
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Created on Wed Feb 17 23:44:18 2021
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Author: Josef Perktold
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License: BSD-3
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"""
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import numpy as np
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from numpy.testing import assert_allclose, assert_array_less
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from scipy import stats
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from statsmodels.distributions.copula.api import (
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CopulaDistribution, ArchimedeanCopula)
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from statsmodels.distributions.copula.api import transforms as tra
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import statsmodels.distributions.tools as dt
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from statsmodels.distributions.bernstein import (
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BernsteinDistribution, BernsteinDistributionBV, BernsteinDistributionUV)
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def test_bernstein_distribution_1d():
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grid = dt._Grid([501])
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loc = grid.x_flat == 0
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grid.x_flat[loc] = grid.x_flat[~loc].min() / 2
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grid.x_flat[grid.x_flat == 1] = 1 - grid.x_flat.min()
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distr = stats.beta(3, 5)
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cdf_g = distr.cdf(np.squeeze(grid.x_flat))
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bpd = BernsteinDistribution(cdf_g)
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cdf_bp = bpd.cdf(grid.x_flat)
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assert_allclose(cdf_bp, cdf_g, atol=0.005)
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assert_array_less(np.median(np.abs(cdf_bp - cdf_g)), 0.001)
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pdfv = distr.pdf(np.squeeze(grid.x_flat))
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pdf_bp = bpd.pdf(grid.x_flat)
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assert_allclose(pdf_bp, pdfv, atol=0.02)
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assert_array_less(np.median(np.abs(pdf_bp - pdfv)), 0.01)
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# compare with UV class
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xf = np.squeeze(grid.x_flat) # UV returns column if x is column
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bpd1 = BernsteinDistributionUV(cdf_g)
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cdf_bp1 = bpd1.cdf(xf)
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assert_allclose(cdf_bp1, cdf_bp, atol=1e-13)
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pdf_bp1 = bpd1.pdf(xf)
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assert_allclose(pdf_bp1, pdf_bp, atol=1e-13)
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cdf_bp1 = bpd1.cdf(xf, method="beta")
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assert_allclose(cdf_bp1, cdf_bp, atol=1e-13)
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pdf_bp1 = bpd1.pdf(xf, method="beta")
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assert_allclose(pdf_bp1, pdf_bp, atol=1e-13)
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cdf_bp1 = bpd1.cdf(xf, method="bpoly")
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assert_allclose(cdf_bp1, cdf_bp, atol=1e-13)
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pdf_bp1 = bpd1.pdf(xf, method="bpoly")
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assert_allclose(pdf_bp1, pdf_bp, atol=1e-13)
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# check rvs
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# currently smoke test
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rvs = bpd.rvs(100)
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assert len(rvs) == 100
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def test_bernstein_distribution_2d():
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grid = dt._Grid([51, 51])
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cop_tr = tra.TransfFrank
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args = (2,)
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ca = ArchimedeanCopula(cop_tr())
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distr1 = stats.uniform
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distr2 = stats.uniform
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cad = CopulaDistribution(ca, [distr1, distr2], cop_args=args)
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cdfv = cad.cdf(grid.x_flat, args)
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cdf_g = cdfv.reshape(grid.k_grid)
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bpd = BernsteinDistribution(cdf_g)
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cdf_bp = bpd.cdf(grid.x_flat)
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assert_allclose(cdf_bp, cdfv, atol=0.005)
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assert_array_less(np.median(np.abs(cdf_bp - cdfv)), 0.001)
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grid_eps = dt._Grid([51, 51], eps=1e-8)
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pdfv = cad.pdf(grid_eps.x_flat)
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pdf_bp = bpd.pdf(grid_eps.x_flat)
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assert_allclose(pdf_bp, pdfv, atol=0.01, rtol=0.04)
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assert_array_less(np.median(np.abs(pdf_bp - pdfv)), 0.05)
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# check marginal cdfs
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# get marginal cdf
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xx = np.column_stack((np.linspace(0, 1, 5), np.ones(5)))
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cdf_m1 = bpd.cdf(xx)
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assert_allclose(cdf_m1, xx[:, 0], atol=1e-13)
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xx = np.column_stack((np.ones(5), np.linspace(0, 1, 5)))
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cdf_m2 = bpd.cdf(xx)
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assert_allclose(cdf_m2, xx[:, 1], atol=1e-13)
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xx_ = np.linspace(0, 1, 5)
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xx = xx_[:, None] # currently requires 2-dim
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bpd_m1 = bpd.get_marginal(0)
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cdf_m1 = bpd_m1.cdf(xx)
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assert_allclose(cdf_m1, xx_, atol=1e-13)
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pdf_m1 = bpd_m1.pdf(xx)
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assert_allclose(pdf_m1, np.ones(len(xx)), atol=1e-13)
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bpd_m = bpd.get_marginal(1)
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cdf_m = bpd_m.cdf(xx)
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assert_allclose(cdf_m, xx_, atol=1e-13)
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pdf_m = bpd_m.pdf(xx)
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assert_allclose(pdf_m, np.ones(len(xx)), atol=1e-13)
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class TestBernsteinBeta2d:
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@classmethod
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def setup_class(cls):
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grid = dt._Grid([91, 101])
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cop_tr = tra.TransfFrank
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args = (2,)
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ca = ArchimedeanCopula(cop_tr())
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distr1 = stats.beta(4, 3)
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distr2 = stats.beta(4, 4) # (5, 2)
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cad = CopulaDistribution(ca, [distr1, distr2], cop_args=args)
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cdfv = cad.cdf(grid.x_flat, args)
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cdf_g = cdfv.reshape(grid.k_grid)
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cls.grid = grid
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cls.cdfv = cdfv
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cls.distr = cad
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cls.bpd = BernsteinDistributionBV(cdf_g)
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def test_basic(self):
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bpd = self.bpd
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grid = self.grid
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cdfv = self.cdfv
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distr = self.distr
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if grid.x_flat.shape[0] < 51**2:
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cdf_bp = bpd.cdf(grid.x_flat)
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assert_allclose(cdf_bp, cdfv, atol=0.05)
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assert_array_less(np.median(np.abs(cdf_bp - cdfv)), 0.01)
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grid_eps = dt._Grid([51, 51], eps=1e-2)
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cdfv = distr.cdf(grid_eps.x_flat)
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cdf_bp = bpd.cdf(grid_eps.x_flat)
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assert_allclose(cdf_bp, cdfv, atol=0.01, rtol=0.01)
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assert_array_less(np.median(np.abs(cdf_bp - cdfv)), 0.05)
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pdfv = distr.pdf(grid_eps.x_flat)
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pdf_bp = bpd.pdf(grid_eps.x_flat)
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assert_allclose(pdf_bp, pdfv, atol=0.06, rtol=0.1)
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assert_array_less(np.median(np.abs(pdf_bp - pdfv)), 0.05)
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def test_rvs(self):
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# currently smoke test
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rvs = self.bpd.rvs(100)
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assert len(rvs) == 100
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class TestBernsteinBeta2dd(TestBernsteinBeta2d):
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@classmethod
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def setup_class(cls):
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grid = dt._Grid([91, 101])
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cop_tr = tra.TransfFrank
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args = (2,)
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ca = ArchimedeanCopula(cop_tr())
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distr1 = stats.beta(4, 3)
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distr2 = stats.beta(4, 4) # (5, 2)
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cad = CopulaDistribution(ca, [distr1, distr2], cop_args=args)
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cdfv = cad.cdf(grid.x_flat, args)
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cdf_g = cdfv.reshape(grid.k_grid)
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cls.grid = grid
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cls.cdfv = cdfv
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cls.distr = cad
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cls.bpd = BernsteinDistribution(cdf_g)
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