"""T-Copula."""
import numpy
from scipy import special
from .baseclass import Copula
from ..baseclass import Dist
class t_copula(Dist):
"""T-Copula."""
def __init__(self, df, R):
C = numpy.linalg.cholesky(R)
Ci = numpy.linalg.inv(C)
self.length = len(R)
Dist.__init__(self, df=df, C=C, Ci=Ci)
def __len__(self):
return self.length
def _cdf(self, x, df, C, Ci):
out = special.stdtr(df, numpy.dot(Ci, special.stdtrit(df, x)))
return out
def _ppf(self, q, df, C, Ci):
out = special.stdtr(df, numpy.dot(C, special.stdtrit(df, q)))
return out
def _lower(self, df, C, Ci):
return 0.
def _upper(self, df, C, Ci):
return 1.
class TCopula(Copula):
"""
T-Copula.
Args:
dist (Dist):
The Distribution to wrap in a copula.
R (numpy.ndarray):
Covariance matrix defining dependencies..
df (float):
The degree of freedom in the underlying student-t distribution.
Examples:
>>> distribution = chaospy.TCopula(
... chaospy.Iid(chaospy.Uniform(-1, 1), 2),
... df=5, R=[[1, .5], [.5, 1]])
>>> distribution
TCopula(Iid(Uniform(lower=-1, upper=1), 2), R=[[1, 0.5], [0.5, 1]], df=5)
>>> samples = distribution.sample(3)
>>> samples.round(4)
array([[ 0.3072, -0.77 , 0.9006],
[ 0.1274, 0.3147, 0.1928]])
>>> distribution.pdf(samples).round(4)
array([0.2932, 0.1367, 0.1969])
>>> distribution.fwd(samples).round(4)
array([[0.6536, 0.115 , 0.9503],
[0.4822, 0.8725, 0.2123]])
>>> mesh = numpy.meshgrid([.4, .5, .6], [.4, .5, .6])
>>> distribution.inv(mesh).round(4)
array([[[-0.2 , 0. , 0.2 ],
[-0.2 , 0. , 0.2 ],
[-0.2 , 0. , 0.2 ]],
<BLANKLINE>
[[-0.2699, -0.1738, -0.0741],
[-0.1011, 0. , 0.1011],
[ 0.0741, 0.1738, 0.2699]]])
>>> distribution.mom([1, 1]).round(4)
0.1665
"""
def __init__(self, dist, df, R):
self._repr = {"df": df, "R": R}
Copula.__init__(self, dist=dist, trans=t_copula(df, R))
