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 12 条

[1] On probability generating functions for waiting time distributions of compound patterns in a sequence of multistate trials
Fu, JC
Chang, YM
JOURNAL OF APPLIED PROBABILITY, 2002, 39 (01) : 70 - 80
[2] On waiting time distributions associated with compound patterns in a sequence of multi-state trials
Kiyoshi Inoue
Sigeo Aki
Annals of the Institute of Statistical Mathematics, 2009, 61 : 499 - 516
[3] On waiting time distributions associated with compound patterns in a sequence of multi-state trials
Inoue, Kiyoshi
Aki, Sigeo
ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS, 2009, 61 (02) : 499 - 516
[4] Generating Functions of Waiting Times and Numbers of Visits for Random Walks on Graphs
Kiyoshi Inoue
Sigeo Aki
Balakrishnan Narayanaswamy
Methodology and Computing in Applied Probability, 2013, 15 : 349 - 362
[5] Generating Functions of Waiting Times and Numbers of Visits for Random Walks on Graphs
Inoue, Kiyoshi
Aki, Sigeo
Narayanaswamy, Balakrishnan
METHODOLOGY AND COMPUTING IN APPLIED PROBABILITY, 2013, 15 (02) : 349 - 362
[6] Distribution and double generating function of number of patterns in a sequence of Markov dependent multistate trials
Chang, Yung-Ming
Fu, James C.
Lin, Han-Ying
ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS, 2012, 64 (01) : 55 - 68
[7] Distribution and double generating function of number of patterns in a sequence of Markov dependent multistate trials
Yung-Ming Chang
James C. Fu
Han-Ying Lin
Annals of the Institute of Statistical Mathematics, 2012, 64 : 55 - 68
[8] On ordered series and later waiting time distributions in a sequence of Markov dependent multistate trials
Fu, JC
Chang, YM
JOURNAL OF APPLIED PROBABILITY, 2003, 40 (03) : 623 - 642
[9] Joint Distributions of Numbers of Runs of Specified Lengths in a Sequence of Markov Dependent Multistate Trials
Kiyoshi Inoue
Sigeo Aki
Annals of the Institute of Statistical Mathematics, 2007, 59 : 577 - 595
[10] On sooner and later waiting time distributions associated with simple patterns in a sequence of bivariate trials
Inoue, Kiyoshi
Aki, Sigeo
METRIKA, 2014, 77 (07) : 895 - 920

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