Compositional (version 1.2)

diri.nr: Fitting a Dirichlet distribution via Newton-Rapshon

Description

Fitting a Dirichlet distribution via Newton-Rapshon.

Usage

diri.nr(x)

Arguments

x

A matrix containing the compositional data.

Value

• A list including:
• iter
  The number of iterations required.
• loglik
  The value of the log-likelihood.
• param
  The estimated parameters.
• runtime
  The run time of the procedure.

Details

Maximum likelihood estimation of the parameters of a Dirichlet distribution is performed via Newton-Raphson. Initial values suggested by Minka (2003) are used. The estimatation is super faster than "diri.est" and the difference becomes really apparent when the sample size and or the dimensions increase. In fact this will work with millions of observations. So in general, I trust this one more than "diri.est". The only problem I have seen with this method is that if the data are concentrated around a point, say the center of the simplex, it will be hard for this and the previous methods to give estimates of the parameters. In this extremely difficult scenario I would suggest the use of the previous function with the precision parametrisation "diri.est(x, type = "prec")". It will be extremely fast and accurate.

References

Thomas P. Minka (2003). Estimating a Dirichlet distribution. http://research.microsoft.com/en-us/um/people/minka/papers/dirichlet/minka-dirichlet.pdf

See Also

diri.est, diri.contour rdiri

Examples

x = rdiri( 100, c(5, 7, 1, 3, 10, 2, 4) )
diri.nr(x)
diri.est(x)