Abstract: Wereconsiderthe Dirichlet model
for the random division of an interval. Thismodelisparameterized bynumber of fragments, together with
a set of positive parameters Its main remarkable properties are
recalled, developed and illustrated.
Explicit results onthe statistical structure of its size-biased permutation are
then obtained. This distribution appears in the sorting of items problem under
the move-to-front rule. Assuming the parameters satisfy as itisshownthat the Dirichlet distribution has a Dirichlet-Kingman non-degenerate
weak limit whose properties are briefly outlined.
Keywords and phrases: random discrete distribution, asymmetric Dirichlet
partition,size-biased permutation, gamma
subordinator, Dirichlet-Kingman partition.
