On generating functions of waiting times and numbers of occurrences of compound patterns in a sequence of multistate trials

被引：4

作者：

Inoue, Kiyoshi

Aki, Sigeo

机构：

[1] Seikei Univ, Fac Econ, Musashino, Tokyo 1808633, Japan

[2] Kansai Univ, Fac Engn, Dept Math, Suita, Osaka 5648680, Japan

来源：

JOURNAL OF APPLIED PROBABILITY | 2007年 / 44卷 / 01期

关键词：

compound pattern; multistate trial; sooner waiting time; later waiting time; run; enumeration scheme; probability function; probability generating function; double generating function;

D O I：

10.1239/jap/1175267164

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

In this paper we study two distributions, namely the distribution of the waiting times until given numbers of occurrences of compound patterns and the distribution of the numbers of occurrences of compound patterns in a fixed number of trials. We elucidate the interrelation between these two distributions in terms of the generating functions. We provide perspectives on the problems related to compound patterns in statistics and probability. As an application, the waiting time problem of counting runs of specified lengths is considered in order to illustrate how the distributions of waiting times can be derived from our theoretical results.

引用

页码：71 / 81

页数：11

共 26 条

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