A Generalized Dirichlet Distribution Accounting for Singularities of the Variables
Peter Lewy · Biometrics · 1996
A multivariate generalized Dirichlet distribution has been formulated for the case where the stochastic variables are allowed to have singularities at 0 and 1. Small sample properties of the estimates of moments of the variables based on maximum likelihood estimates of the parameters have been compared to the empirical moments. In general the estimates 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 the variables. In cases with many zero occurrences of the variables, the empirical moments are just as efficient as ML and may therefore be used instead of ML. As an illustration, the model has been applied to estimate the species composition in the Danish industrial fishery.