A GENERALIZED DIRICHLET DISTRIBUTION ACCOUNTING FOR SINGULARITIES OF THE VARIABLES

A multivariate generalized Dirichlet distribution has been formulated for the case where the stochastic variables are allowed to have singul arities at 0 and 1. Small sample properties of the estimates of moment s of the variables based on maximum likelihood estimates of the parame ters have been compared to the empirical moments. In general the estim ates based on maximum likelihood are superior to the empirical moments in the small sample case. However, the main advantage of ML is not in computing the mean value, but rather in estimating the precision of t he variables. In cases with many zero occurrences of the variables, th e empirical moments are just as efficient as ML and may therefore be u sed instead of hit. As an illustration, the model has been applied to estimate the species composition in the Danish industrial fishery.