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 \mu_{i,m}, 1\le i \le p, 1\le m \le 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 nu_m, 1\le m \le 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 1.0.5 Index]