ddirimix: Angular density/likelihood function in the Dirichlet Mixture... In lbelzile/BMAmevt: Multivariate Extremes: Bayesian Estimation of the Spectral Measure

Description

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

Usage

 ```1 2 3 4 5``` ```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.

lbelzile/BMAmevt documentation built on June 13, 2019, 12:43 p.m.