Fitting a Dirichlet distribution via Newton-Rapshon
Fitting a Dirichlet distribution via Newton-Rapshon.
diri.nr2(x, type = 1, tol = 1e-07)
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. |
Maximum likelihood estimation of the parameters of a Dirichlet distribution is performed via Newton-Raphson. Initial values suggested by Minka (2012) are used.
A list including:
loglik |
The value of the log-likelihood. |
param |
The estimated parameters. |
Michail Tsagris and Manos Papadakis
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Manos Papadakis <papadakm95@gmail.com>
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.
x <- matrix( rgamma(100 * 4, c(5, 6, 7, 8), 1), ncol = 4) x <- x / rowsums(x) res<-diri.nr2(x)
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