COPULAFIT Fit a parametric copula to data.
RHOHAT = COPULAFIT('Gaussian', U) returns an estimate RHOHAT of the matrix
of linear correlation parameters for a Gaussian copula, given data in U. U
is an N-by-P matrix of values in (0,1), representing N points in the
P-dimensional unit hypercube.
[RHOHAT, NUHAT] = COPULAFIT('t', U) returns an estimate RHOHAT of the matrix
of linear correlation parameters for a t copula, and an estimate NUHAT of
the degrees of freedom parameter, given data in U. U is an N-by-P matrix of
values in (0,1), representing N points in the P-dimensional unit hypercube.
[RHOHAT, NUHAT, NUCI] = COPULAFIT('t', U) returns an approximate 95%
confidence interval for the degrees of freedom parameter for a t copula,
given data in U.
PARAMHAT = COPULAFIT(FAMILY, U) returns an estimate PARAMHAT of the copula
parameter for an Archimedean copula specified by FAMILY, given data in U. U
is an N-by-2 matrix of values in (0,1), representing N points in the unit
square. FAMILY is 'Clayton', 'Frank', or 'Gumbel'.
[PARAMHAT, PARAMCI] = COPULAFIT(FAMILY, U) returns an approximate 95%
confidence interval for the copula parameter from an Archimedean copula
specified by FAMILY, given data in U.
[...] = COPULAFIT(..., 'Alpha', ALPHA) returns an approximate 100(1-ALPHA)%
confidence interval for the parameter estimate.
COPULAFIT uses maximum likelihood to fit the copula to U. When U contains
data transformed to the unit hypercube by parametric estimates of their
marginal cumulative distribution functions, this is known as the Inference
Functions for Margins (IFM) method. When U contains data transformed by
the empirical CDF, this is known as Canonical Maximum Likelihood (CML).
[...] = COPULAFIT('t', U, ..., 'Method', 'ApproximateML') fits a t copula by
maximizing an objective function, as suggested by Bouye et al., that
approximates the profile log-likelihood for the degrees of freedom parameter
nu, for large sample sizes. This method can be significantly faster than
using maximum likelihood, however, it should be used with caution because
the estimates and confidence limits may not be accurate for small or
moderate sample sizes. COPULAFIT('t', U, ..., 'Method', 'ML') is equivalent
to the default maximum likelihood fit.
[...] = COPULAFIT(..., 'Options', OPTIONS) specifies control parameters for
the iterative algorithm used to compute estimates. This argument can be
created by a call to STATSET. See STATSET('copulafit') for parameter names
and default values. This argument does not apply to the 'Gaussian' family.
See also ecdf, copulacdf, copulapdf, copularnd.
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