dnestlog.grid {BMAmevt} R Documentation

## PB and NL spectral densities on the two-dimensional simplex

### Description

The two functions compute respectively the NL and PB spectral densities, in the three-dimensional case, on a discretization grid. A plot is issued (optional).

### Usage

```dnestlog.grid(
par,
npoints = 50,
eps = 0.001,
equi = TRUE,
displ = TRUE,
invisible = TRUE,
...
)

dpairbeta.grid(
par,
npoints = 50,
eps = 0.001,
equi = TRUE,
displ = TRUE,
invisible = TRUE,
...
)
```

### Arguments

 `par` The parameter for the Pairwise Beta or the Nested Logistic density. In the Pairwise Beta model, `par` is of length `choose(p,2)+1`. The first element is the global dependence parameter, the subsequent ones are the pairwise dependence parameters, in lexicographic order (e.g. β_{12}, β_{13}, β_{23}). In the NL model, `par` is a vector of length four with components between zero and one. The first one is the global dependence parameter, the three subsequent ones are the pairwise dependence parameters, again in lexicographic order. `npoints` The number of grid nodes on the squared grid containing the desired triangle. `eps` Positive number: minimum distance from any node inside the simplex to the simplex boundary `equi` logical. Is the simplex represented as an equilateral triangle (if `TRUE`) or a right triangle (if `FALSE`) ? `displ` logical. Should a plot be produced ? `invisible` logical. If `TRUE`, the result is returned as `invisible`. `...` Additional arguments to be passed to `dgridplot`

### Value

A `npoints*npoints` matrix containing the considered density's values on the grid. The row (resp. column) indices increase with the first (resp. second) coordinate on the simplex.

### Note

If `equi==TRUE`, the density is relative to the Hausdorff measure on the simplex itself: the values obtained with `equi = FALSE` are thus divided by √ 3.

### Examples

```
dpairbeta.grid(par=c( 0.8, 8, 5, 2),
npoints=70, eps = 1e-3, equi = TRUE, displ = TRUE, invisible=TRUE)

##  or ...

Dens <- dpairbeta.grid(par=c(0.8, 8, 5, 2),
npoints=70, eps = 1e-3, equi = TRUE, displ = FALSE)
Grid=discretize(npoints=70,eps=1e-3,equi=TRUE)
dev.new()
image(Grid\$X, Grid\$Y, Dens)
contour(Grid\$X, Grid\$Y, Dens, add=TRUE)
add.frame(equi=TRUE, npoints=70, axes=FALSE)

```

[Package BMAmevt version 1.0.4 Index]