| DensityGenerator.normalize {ElliptCopulas} | R Documentation |
Normalization of an elliptical copula generator
Description
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.
Usage
DensityGenerator.normalize(grid, grid_g, d, verbose = 0, b = 1)
DensityGenerator.check(grid, grid_g, d, b = 1)
Arguments
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. |
Value
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.
References
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.
See Also
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.