| DensityGenerator.normalize {ElliptCopulas} | R Documentation |
The function DensityGenerator.normalize transforms an elliptical copula generator
into an elliptical copula generator,generating the same distribution
and which is normalized to follow the normalization constraint
\frac{\pi^{d/2}}{\Gamma(d/2)}
\int_0^{+\infty} g_k(t) t^{(d-2)/2} dt = 1.
as well as the identification constraint
\frac{\pi^{(d-1)/2}}{\Gamma((d-1)/2)}
\int_0^{+\infty} g_k(t) t^{(d-3)/2} dt = b.
The function DensityGenerator.check checks, for a given generator,
whether these two constraints are satisfied.
DensityGenerator.normalize(grid, grid_g, d, verbose = 0, b = 1)
DensityGenerator.check(grid, grid_g, d, b = 1)
grid |
the regularly spaced grid on which the values of the generator are given. |
grid_g |
the values of the |
d |
the dimension of the space. |
verbose |
if 1, prints the estimated (alpha, beta) such that
|
b |
the target value for the identification constraint. |
DensityGenerator.normalize returns
the normalized generator, as a list of values on the same grid.
DensityGenerator.check returns (invisibly) a vector of two booleans
where the first element is TRUE if the normalization constraint is satisfied
and the second element is TRUE if the identification constraint is satisfied.
Derumigny, A., & Fermanian, J. D. (2022). Identifiability and estimation of meta-elliptical copula generators. Journal of Multivariate Analysis, article 104962. doi:10.1016/j.jmva.2022.104962.
EllCopSim() for the simulation of elliptical copula samples,
EllCopEst() for the estimation of elliptical copula,
conversion functions for the conversion between different representation
of the generator of an elliptical copula.