ddirimix {BMAmevt} R Documentation

## Angular density/likelihood function in the Dirichlet Mixture model.

### Description

Likelihood function (spectral density on the simplex) and angular data sampler in the Dirichlet mixture model.

### Usage

```ddirimix(
x = c(0.1, 0.2, 0.7),
par,
wei = par\$wei,
Mu = par\$Mu,
lnu = par\$lnu,
log = FALSE,
vectorial = FALSE
)

rdirimix(
n = 10,
par = get("dm.expar.D3k3"),
wei = par\$wei,
Mu = par\$Mu,
lnu = par\$lnu
)
```

### Arguments

 `x` An angular data set which may be reduced to a single point: A n*p matrix or a vector of length `p`, where p is the dimension of the sample space and n is the sample size. Each row is a point on the simplex, so that each row sum to one. The error tolerance is set to `1e-8` in this package. `par` The parameter list for the Dirichlet mixture model. `wei` Optional. If present, overrides the value of `par\$wei`. `Mu` Optional. If present, overrides the value of `par\$Mu`. `lnu` Optional. If present, overrides the value of `par\$lnu`. `log` Logical: should the density or the likelihood be returned on the log-scale ? `vectorial` Logical: Should a vector of size n or a single value be returned ? `n` The number of angular points to be generated

### Details

The spectral probability measure defined on the simplex characterizes the dependence structure of multivariate extreme value models. The parameter list for a mixture with k components, is made of

Mu

The density kernel centers μ[1:p,1:k] : A p*k matrix, which columns sum to one, and such that `Mu %*% wei=1`, for the moments constraint to be satisfied. Each column is a Dirichlet kernel center.

wei

The weights vector for the kernel densities: A vector of k positive numbers summing to one.

lnu

The logarithms of the shape parameters ν[1:k] for the density kernels: a vector of size k.

The moments constraint imposes that the barycenter of the columns in `Mu`, with weights `wei`, be the center of the simplex.

### Value

`ddirimix` returns the likelihood as a single number if `vectorial ==FALSE`, or as a vector of size `nrow(x)` containing the likelihood of each angular data point. If `log == TRUE`, the log-likelihood is returned instead. `rdirimix` returns a matrix with `n` points and `p=nrow(Mu)` columns.

[Package BMAmevt version 1.0.4 Index]