123 lines
3.4 KiB
Python
123 lines
3.4 KiB
Python
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"""
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Created on Fri Jan 29 19:19:45 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 scipy import stats
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from statsmodels.tools.rng_qrng import check_random_state
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from statsmodels.distributions.copula.copulas import Copula
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class IndependenceCopula(Copula):
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"""Independence copula.
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Copula with independent random variables.
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.. math::
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C_\theta(u,v) = uv
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Parameters
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----------
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k_dim : int
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Dimension, number of components in the multivariate random variable.
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Notes
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-----
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IndependenceCopula does not have copula parameters.
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If non-empty ``args`` are provided in methods, then a ValueError is raised.
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The ``args`` keyword is provided for a consistent interface across
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copulas.
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"""
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def __init__(self, k_dim=2):
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super().__init__(k_dim=k_dim)
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def _handle_args(self, args):
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if args != () and args is not None:
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msg = ("Independence copula does not use copula parameters.")
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raise ValueError(msg)
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else:
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return args
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def rvs(self, nobs=1, args=(), random_state=None):
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self._handle_args(args)
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rng = check_random_state(random_state)
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x = rng.random((nobs, self.k_dim))
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return x
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def pdf(self, u, args=()):
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u = np.asarray(u)
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return np.ones(u.shape[:-1])
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def cdf(self, u, args=()):
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return np.prod(u, axis=-1)
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def tau(self):
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return 0
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def plot_pdf(self, *args):
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raise NotImplementedError("PDF is constant over the domain.")
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def rvs_kernel(sample, size, bw=1, k_func=None, return_extras=False):
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"""Random sampling from empirical copula using Beta distribution
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Parameters
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----------
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sample : ndarray
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Sample of multivariate observations in (o, 1) interval.
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size : int
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Number of observations to simulate.
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bw : float
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Bandwidth for Beta sampling. The beta copula corresponds to a kernel
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estimate of the distribution. bw=1 corresponds to the empirical beta
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copula. A small bandwidth like bw=0.001 corresponds to small noise
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added to the empirical distribution. Larger bw, e.g. bw=10 corresponds
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to kernel estimate with more smoothing.
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k_func : None or callable
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The default kernel function is currently a beta function with 1 added
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to the first beta parameter.
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return_extras : bool
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If this is False, then only the random sample will be returned.
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If true, then extra information is returned that is mainly of interest
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for verification.
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Returns
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-------
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rvs : ndarray
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Multivariate sample with ``size`` observations drawn from the Beta
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Copula.
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Notes
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-----
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Status: experimental, API will change.
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"""
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# vectorized for observations
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n = sample.shape[0]
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if k_func is None:
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kfunc = _kernel_rvs_beta1
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idx = np.random.randint(0, n, size=size)
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xi = sample[idx]
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krvs = np.column_stack([kfunc(xii, bw) for xii in xi.T])
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if return_extras:
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return krvs, idx, xi
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else:
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return krvs
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def _kernel_rvs_beta(x, bw):
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# Beta kernel for density, pdf, estimation
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return stats.beta.rvs(x / bw + 1, (1 - x) / bw + 1, size=x.shape)
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def _kernel_rvs_beta1(x, bw):
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# Beta kernel for density, pdf, estimation
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# Kiriliouk, Segers, Tsukuhara 2020 arxiv, using bandwith 1/nobs sample
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return stats.beta.rvs(x / bw, (1 - x) / bw + 1)
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