Fitting a Dirichlet distribution via Newton-Rapshon {Rfast}

Fitting a Dirichlet distribution via Newton-Rapshon

Description

Fitting a Dirichlet distribution via Newton-Rapshon.

Usage

diri.nr2(x, type = 1, tol = 1e-07)

Arguments

x

A matrix containing the compositional data. Zeros are not allowed.

type

Type 1 uses a vectorised version of the Newton-Raphson (Minka, 2012). In high dimensions this is to be preferred. If the data are too concentrated, regardless of the dimensions, this is also to be preferrred. Type 2 uses the regular Newton-Raphson, with matrix multiplications. In small dimensions this can be considerably faster.

tol

The tolerance level idicating no further increase in the log-likelihood.

Details

Maximum likelihood estimation of the parameters of a Dirichlet distribution is performed via Newton-Raphson. Initial values suggested by Minka (2012) are used.

Value

A list including:

loglik

The value of the log-likelihood.

param

The estimated parameters.

Author(s)

Michail Tsagris and Manos Papadakis

R implementation and documentation: Michail Tsagris <[e-mail]> and Manos Papadakis <[e-mail]>

References

Minka Thomas (2012). Estimating a Dirichlet distribution. Technical report.

Ng Kai Wang, Guo-Liang Tian, and Man-Lai Tang (2011). Dirichlet and related distributions: Theory, methods and applications. John Wiley & Sons.

See Also

beta.mle

Examples

x <- matrix( rgamma(100 * 4, c(5, 6, 7, 8), 1), ncol = 4)
x <- x / rowsums(x)
res<-diri.nr2(x)