No. 1114

Title:

Distributions of simple patterns in some kinds of exchangeable sequence

Author(s):

Inoue, Kiyoshi (Faculty of Economics, Seikei University);
Aki, Sigeo (Faculty of Engineering Science, Kansai University);
Hirano, Katuomi (Faculty of Science, Josai University)

Key words:

Pattern, scan, run, exchangeable multi-state trials, enumeration schemes, conditional distribution, probability function, probability generating function, double generating function.

Abstract:

    In this article, we consider the distributions of simple patterns in some types of sequences of infinite exchangeable multistate trials. The distributions on exchangeable multistate trials are considered in terms of an extension of de Finetti's theorem. As an application of partially exchangeable sequences, distributions on a Markov exchangeable sequence are studied. Furthermore, we propose a new type of partially exchangeable sequence and examine its properties. In addition, we discuss the distribution theory in the case of the finite exchangeable sequences. The results presented here provide a wide framework for developing the exact distribution theory of simple patterns. Finally, some examples are given in order to illustrate our theoretical results.