ddirimix {BMAmevt}

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.