A Species Sampling Model with Finitely many Types

A two-parameter family of exchangeable partitions with a simple updating rule is introduced. The partition is identified with a randomized version of a standard symmetric Dirichlet species-sampling model with finitely many types. A power-like distribution for the number of types is derived

Coherent random permutations with record statistics

Random permutations with distribution conditionally uniform given the set of record values can be generated in a unified way, coherently for all values of $n$. Our central example is a two-parameter family of random permutations that are conditionally uniform given the counts of upper and lower records. This family interpolates between two versions of Ewens' distribution. We discuss characterisations of the conditionally uniform permutations, their asymptotic properties, constructions and relations to random partitions.Comment: 17 page

Constrained exchangeable partitions

For a class of random partitions of an infinite set a de Finetti-type representation is derived, and in one special case a central limit theorem for the number of blocks is shown