conv_funct {ElliptCopulas} | R Documentation |

## Conversion Functions for Elliptical Distributions

### Description

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.

### Usage

```
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)
```

### Arguments

`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 |

### Value

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`

.

### See Also

`DensityGenerator.normalize`

to compute the normalized version of a given `d`

-dimensional generator.

### Examples

```
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))
```

*ElliptCopulas*version 0.1.3 Index]