maximum_likelihood: Maximum likelihood point for the hyperdirichlet distribution
In hyperdirichlet: A Generalization of the Dirichlet Distribution

Description Usage Arguments Details Value Note Author(s) See Also Examples

Maximum likelihood point for the hyperdirichlet distribution as estimated using numerical maximization.

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maximum_likelihood(HD, start_p = NULL, give = FALSE, disallowed = NULL, zero=NULL, ...)
               mle(HD, start_p = NULL, give = FALSE, disallowed = NULL,            ...)
    mle_restricted(HD, start_p = NULL, give = FALSE, disallowed = NULL, zero=NULL, ...)

`HD`	Object of class hyperdirichlet
`start_p`	Start value for the `p`s. See details section
`give`	Boolean with default `FALSE` meaning to return just the point estimate and `TRUE` meaning to return all the output from `optim()`
`disallowed`	A function of `p` returning a Boolean to restrict the search for the MLE. See examples
`zero`	In function `maxlike_restricted()`, a Boolean vector with `TRUE` elements corresponding to components that are constrained to be zero. See details section
`...`	Further arguments sent to `optim()`

The user should use function maximum_likelihood(), which is a user-friendly wrapper for one of the two functions (mle() or mle_rst()) depending on whether argument zero is or is not NULL.

Argument start_p specifies the start point for the optimization; default NULL is interpreted as rep(1/n,n) where n is dim(HD) (ie neutral position).

It is not necessary to normalize start_p: this is done by dhyperdirichlet().

Non-default values for this argument are interpreted by dhyperdirichlet().

Argument zero, if not default NULL, is Boolean in the standard case; but if it is not Boolean, it is interpreted as a numeric vector of integers indicating which components of the distribution are restricted to zero. An example is given below.

Returns a k-tuple.

The functions minimize -dhyperdirichlet(...,log=TRUE); so there is no need to set fnscale.

Be aware that the aylmer package includes a function maxlike(), which does something different.

Robin K. S. Hankin

dhyperdirichlet_p,optim

maximum_likelihood(dirichlet(1:4))      # Should be 0:3

jj.numerical <- maximum_likelihood(dirichlet(3:8), zero=2:3)$MLE

jj <- c(2,0,0,5,6,7)
jj.analytical <- jj/sum(jj)

jj.numerical - jj.analytical  # should be small