Example #1
0
def test_pdf():
    '''
    Tests the probability density function.
    '''
    samples = np.array([np.linspace(0, 1, 5), np.linspace(0.2, 0.8, 5)]).T

    # Independence copula
    independence_copula = IndependenceCopula()
    # Comparison values
    r_pdf = np.array([0.0, 1.0, 1.0, 1.0, 0.0])
    p_pdf = independence_copula.pdf(samples)
    assert_allclose(p_pdf, r_pdf)

    # Gaussian copula family
    gaussian_copula = GaussianCopula(0.5)
    # Comparison values
    r_pdf = np.array([0.0, 1.2417679440, 1.1547005384, 1.2417679440, 0.0])
    p_pdf = gaussian_copula.pdf(samples)
    assert_allclose(p_pdf, r_pdf)

    # Clayton copula family
    clayton_copula = ClaytonCopula(5)
    # Comparison values
    r_pdf = np.array([0.0, 2.1943031503, 2.7037217178, 1.9477508961, 0.0])
    p_pdf = clayton_copula.pdf(samples)
    assert_allclose(p_pdf, r_pdf)

    # Frank copula family
    frank_copula = FrankCopula(5)
    # Comparison values
    r_pdf = np.array([0.0, 1.5167615765, 1.4735637246, 1.5167615765, 0.0])
    p_pdf = frank_copula.pdf(samples)
    assert_allclose(p_pdf, r_pdf)
Example #2
0
def test_cdf():
    '''
    Tests the cumulative distribution function.
    '''
    samples = np.array([np.linspace(0, 1, 5), np.linspace(0.2, 0.8, 5)]).T

    # Independence copula
    independence_copula = IndependenceCopula()
    # Comparison values
    r_cdf = np.array([0.0, 0.0875, 0.25, 0.4875, 0.8])
    p_cdf = independence_copula.cdf(samples)
    assert_allclose(p_cdf, r_cdf)

    # Gaussian copula family
    gaussian_copula = GaussianCopula(0.5)
    # Comparison values
    r_cdf = np.array([0.0, 0.1520333540, 0.3333333333, 0.5520333540, 0.8])
    p_cdf = gaussian_copula.cdf(samples)
    assert_allclose(p_cdf, r_cdf)

    # Clayton copula family
    clayton_copula = ClaytonCopula(5)
    # Comparison values
    r_cdf = np.array([0.0, 0.2416570262, 0.4366484171, 0.6100768349, 0.8])
    p_cdf = clayton_copula.cdf(samples)
    assert_allclose(p_cdf, r_cdf)

    # Frank copula family
    frank_copula = FrankCopula(5)
    # Comparison values
    r_cdf = np.array([0.0, 0.1800378858, 0.3771485107, 0.5800378858, 0.8])
    p_cdf = frank_copula.cdf(samples)
    assert_allclose(p_cdf, r_cdf)
Example #3
0
def test_ppcf():
    '''
    Tests the conditional cumulative distribution function.
    '''
    samples = np.array([np.linspace(0, 1, 5), np.linspace(0.2, 0.8, 5)]).T

    # Independence copula
    independence_copula = IndependenceCopula()
    # Comparison values
    r_ppcf = np.array([0.0, 0.25, 0.5, 0.75, 1.0])
    p_ppcf = independence_copula.ppcf(samples)
    assert_allclose(p_ppcf, r_ppcf)
    # Test other axis
    r_ppcf = np.array([0.2, 0.35, 0.5, 0.65, 0.8])
    p_ppcf = independence_copula.ppcf(samples, axis=0)
    assert_allclose(p_ppcf, r_ppcf)

    # Gaussian copula family
    gaussian_copula = GaussianCopula(0.5)
    # Comparison values
    r_ppcf = np.array([0.0, 0.218642669, 0.5, 0.781357331, 1.0])
    p_ppcf = gaussian_copula.ppcf(samples)
    assert_allclose(p_ppcf, r_ppcf)
    # Test other axis
    r_ppcf = np.array([0.0, 0.2511286797, 0.5, 0.7488713203, 1.0])
    p_ppcf = gaussian_copula.ppcf(samples, axis=0)
    assert_allclose(p_ppcf, r_ppcf)

    # Clayton copula family
    clayton_copula = ClaytonCopula(5)
    # Comparison values
    r_ppcf = np.array([0.0, 0.2994846602, 0.5211309028, 0.7859307932, 1.0])
    p_ppcf = clayton_copula.ppcf(samples)
    assert_allclose(p_ppcf, r_ppcf)
    # Test other axis
    r_ppcf = np.array(
        [0.0, 0.2337467913, 0.5211309028, 0.8127416749, 0.9634924840])
    p_ppcf = clayton_copula.ppcf(samples, axis=0)
    assert_allclose(p_ppcf, r_ppcf)

    # Frank copula family
    frank_copula = FrankCopula(5)
    # Comparison values
    r_ppcf = np.array([0.0, 0.21162507, 0.5, 0.78837493, 1.0])
    p_ppcf = frank_copula.ppcf(samples)
    assert_allclose(p_ppcf, r_ppcf)
    # Test other axis
    r_ppcf = np.array([0.0442921, 0.20900068, 0.5, 0.79099932, 0.9557079])
    p_ppcf = frank_copula.ppcf(samples, axis=0)
    assert_allclose(p_ppcf, r_ppcf)
Example #4
0
def test_ccdf():
    '''
    Tests the conditional cumulative distribution function.
    '''
    samples = np.array([np.linspace(0, 1, 5), np.linspace(0.2, 0.8, 5)]).T

    # Independence copula
    independence_copula = IndependenceCopula()
    # Comparison values
    r_ccdf = np.array([0.0, 0.25, 0.5, 0.75, 1.0])
    p_ccdf = independence_copula.ccdf(samples)
    assert_allclose(p_ccdf, r_ccdf)
    # Test other axis
    r_ccdf = np.array([0.2, 0.35, 0.5, 0.65, 0.8])
    p_ccdf = independence_copula.ccdf(samples, axis=0)
    assert_allclose(p_ccdf, r_ccdf)

    # Gaussian copula family
    gaussian_copula = GaussianCopula(0.5)
    # Comparison values
    r_ccdf = np.array([0.0, 0.2889793807, 0.5, 0.7110206193, 1.0])
    p_ccdf = gaussian_copula.ccdf(samples)
    assert_allclose(p_ccdf, r_ccdf)
    # Test other axis
    r_ccdf = np.array([1.0, 0.4778649221, 0.5, 0.5221350779, 0.0])
    p_ccdf = gaussian_copula.ccdf(samples, axis=0)
    assert_allclose(p_ccdf, r_ccdf)

    # Clayton copula family
    clayton_copula = ClaytonCopula(5)
    # Comparison values
    r_ccdf = np.array([0.0, 0.1083398661, 0.4435793443, 0.6836393756, 1.0])
    p_ccdf = clayton_copula.ccdf(samples)
    assert_allclose(p_ccdf, r_ccdf)
    # Test other axis
    r_ccdf = np.array([0.0, 0.815748922, 0.4435793443, 0.2896940854, 0.262144])
    p_ccdf = clayton_copula.ccdf(samples, axis=0)
    assert_allclose(p_ccdf, r_ccdf)

    # Frank copula family
    frank_copula = FrankCopula(5)
    # Comparison values
    r_ccdf = np.array([0.0, 0.3070854, 0.5, 0.6929146, 1.0])
    p_ccdf = frank_copula.ccdf(samples)
    assert_allclose(p_ccdf, r_ccdf)
    # Test other axis
    r_ccdf = np.array([0.63640865, 0.58629237, 0.5, 0.41370763, 0.36359135])
    p_ccdf = frank_copula.ccdf(samples, axis=0)
    assert_allclose(p_ccdf, r_ccdf)
Example #5
0
def test_logcdf():
    '''
    Tests the log of the cumulative distribution function.
    '''
    samples = np.array([np.linspace(0, 1, 5), np.linspace(0.2, 0.8, 5)]).T

    # Independence copula
    independence_copula = IndependenceCopula()
    # Comparison values
    r_logcdf = np.array(
        [-np.inf, -2.4361164856, -1.3862943611, -0.7184649885, -0.2231435513])
    p_logcdf = independence_copula.logcdf(samples)
    assert_allclose(p_logcdf, r_logcdf)

    # Gaussian copula family
    gaussian_copula = GaussianCopula(0.5)
    # Comparison values
    r_logcdf = np.array(
        [-np.inf, -1.8836553477, -1.0986122887, -0.5941468105, -0.2231435513])
    p_logcdf = gaussian_copula.logcdf(samples)
    assert_allclose(p_logcdf, r_logcdf)

    # Clayton copula family
    clayton_copula = ClaytonCopula(5)
    # Comparison values
    r_logcdf = np.array(
        [-np.inf, -1.4202358053, -0.8286269453, -0.4941703709, -0.2231435513])
    p_logcdf = clayton_copula.logcdf(samples)
    assert_allclose(p_logcdf, r_logcdf)

    # Frank copula family
    frank_copula = FrankCopula(5)
    # Comparison values
    r_logcdf = np.array(
        [-np.inf, -1.7145879734, -0.9751162414, -0.5446618572, -0.2231435513])
    p_logcdf = frank_copula.logcdf(samples)
    assert_allclose(p_logcdf, r_logcdf)
Example #6
0
def test_logpdf():
    '''
    Tests the log of the probability density function.
    '''
    samples = np.array([np.linspace(0, 1, 5), np.linspace(0.2, 0.8, 5)]).T

    # Independence copula
    independence_copula = IndependenceCopula()
    # Comparison values
    r_logpdf = np.array([-np.inf, 0.0, 0.0, 0.0, -np.inf])
    p_logpdf = independence_copula.logpdf(samples)
    assert_allclose(p_logpdf, r_logpdf)

    # Gaussian copula family
    gaussian_copula = GaussianCopula(0.5)
    # Comparison values
    r_logpdf = np.array(
        [-np.inf, 0.2165361255, 0.1438410362, 0.2165361255, -np.inf])
    p_logpdf = gaussian_copula.logpdf(samples)
    assert_allclose(p_logpdf, r_logpdf)

    # Clayton copula family
    clayton_copula = ClaytonCopula(5)
    # Comparison values
    r_logpdf = np.array(
        [-np.inf, 0.7858645247, 0.9946292379, 0.6666753203, -np.inf])
    p_logpdf = clayton_copula.logpdf(samples)
    assert_allclose(p_logpdf, r_logpdf)

    # Frank copula family
    frank_copula = FrankCopula(5)
    # Comparison values
    r_logpdf = np.array(
        [-np.inf, 0.4165775202, 0.3876837693, 0.4165775202, -np.inf])
    p_logpdf = frank_copula.logpdf(samples)
    assert_allclose(p_logpdf, r_logpdf)
Example #7
0
        def fit(self,
                samples,
                is_continuous,
                is_adjusted=None,
                trunc_level=None):
            '''
            Fits the vine tree to the given samples.  This method is supposed
            to be called on the output layer and will recurse to its input
            layers.

            Parameters
            ----------
            samples : array_like
                n-by-d matrix of samples where n is the number of samples and d
                is the number of marginals.
            is_continuous : array_like
                List of boolean values of length d, where d is the number of
                marginals and element i is `True` if marginal i is continuous.
            manual_adjust : array_like
                list of distributions of length d, where d is the number of 
                marginals and element i is a scipy distribution if it was
                adjusted beforehand or None if the program has to ajust it.
            trunc_level : integer, optional
                Layer level to truncate the vine at.  Copulas in layers beyond
                are just independence copulas.  If the level is `None`, then
                the vine is not truncated.  (Default: `None`)

            Returns
            -------
            output_urvs : array_like
                The output uniform random variates of the layer.  Can be
                ignored if this is the output layer.
            '''
            if self.is_marginal_layer():
                output_urvs = np.zeros(samples.shape)
                if is_adjusted:
                    for i in range(samples.shape[1]):
                        self.marginals[i] = Marginal_.fit(
                            samples[:, i], is_continuous[i], is_adjusted[i])
                        output_urvs[:, i] = self.marginals[i].cdf(samples[:,
                                                                          i])
                else:
                    for i in range(samples.shape[1]):
                        self.marginals[i] = Marginal_.fit(
                            samples[:, i], is_continuous[i])
                        output_urvs[:, i] = self.marginals[i].cdf(samples[:,
                                                                          i])
            else:
                input_urvs = self.input_layer.fit(samples, is_continuous,
                                                  is_adjusted)
                truncate = trunc_level and samples.shape[1] \
                    - len(self.input_indices) > trunc_level - 1
                output_urvs = np.zeros(
                    (samples.shape[0], len(self.input_indices)))
                for i, i_ind in enumerate(self.input_indices):
                    if truncate:
                        self.copulas[i] = IndependenceCopula()
                    else:
                        self.copulas[i] = Copula.fit(input_urvs[:, i_ind])
                    output_urvs[:, i] \
                        = self.copulas[i].ccdf(input_urvs[:, i_ind])
            return output_urvs