conv_funct {ElliptCopulas} | R Documentation |
An elliptical random vector X of density |det(\Sigma)|^{-1/2} g_d(x' \Sigma^{-1} x)
can always be written as X = \mu + R * A * U
for some positive random variable R
and a random vector U
on the d
-dimensional sphere.
Furthermore, there is a one-to-one mapping between g_d
and its one-dimensional marginal g_1.
Convert_gd_To_g1(grid, g_d, d)
Convert_g1_To_Fg1(grid, g_1)
Convert_g1_To_Qg1(grid, g_1)
Convert_g1_To_f1(grid, g_1)
Convert_gd_To_fR2(grid, g_d, d)
grid |
the grid on which the values of the functions in parameter are given. |
g_d |
the |
d |
the dimension of the random vector. |
g_1 |
the |
One of the following
g_1 the 1
-dimensional density generator.
Fg1 the 1
-dimensional marginal cumulative distribution function.
Qg1 the 1
-dimensional marginal quantile function
(approximatly equal to the inverse function of Fg1).
f1 the density of a 1
-dimensional margin if \mu = 0
and A
is the identity matrix.
fR2 the density function of R^2
.
DensityGenerator.normalize
to compute the normalized version of a given d
-dimensional generator.
grid = seq(0,100,by = 0.01)
g_d = DensityGenerator.normalize(grid = grid, grid_g = 1/(1+grid^3), d = 3)
g_1 = Convert_gd_To_g1(grid = grid, g_d = g_d, d = 3)
Fg_1 = Convert_g1_To_Fg1(grid = grid, g_1 = g_1)
Qg_1 = Convert_g1_To_Qg1(grid = grid, g_1 = g_1)
f1 = Convert_g1_To_f1(grid = grid, g_1 = g_1)
fR2 = Convert_gd_To_fR2(grid = grid, g_d = g_d, d = 3)
plot(grid, g_d, type = "l", xlim = c(0,10))
plot(grid, g_1, type = "l", xlim = c(0,10))
plot(Fg_1, xlim = c(-3,3))
plot(Qg_1, xlim = c(0.01,0.99))
plot(f1, xlim = c(-3,3))
plot(fR2, xlim = c(0,3))