No. 1061

Title:

Exact Distributions on Discrete Patterns in Some Kinds of Exchangeable Sequences

Author(s):

Aki, Sigeo (Kansai University);
Hirano, Katuomi (The Institute of Statistical Mathematics)

Key words:

Discrete pattern, exchangeability, waiting time, generalized probability generating function, conditional expectation, discrete distribution theory

Abstract:

    Discrete distributions on exchangeable \{ 0,1 \}-valued trials are studied based on de Finetti's theorem. By using an extension of de Finetti's theorem, discrete distributions on exchangeable multistate trials are also investigated. As an application of partial exchangeable sequences, discrete distributions on a Markov exchangeable sequence are also studied. Further, as a new type of partial exchangeable sequence, a binary sequence model is proposed which has partial exchangeability of order $k$. The sequence is a mixture of binary sequences of order $k$ if it is recurrent.