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^{(d2)/2} dt = 1.
as well as the identification constraint
\frac{\pi^{(d1)/2}}{\Gamma((d1)/2)}
\int_0^{+\infty} g_k(t) t^{(d3)/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 metaelliptical 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.