On sooner and later waiting time distributions associated with simple patterns in a sequence of bivariate trials

被引：0
作者：
Kiyoshi Inoue
Sigeo Aki
机构：
[1] Seikei University,Faculty of Economics
[2] Kansai University,Department of Mathematics, Faculty of Engineering Science
来源：
Metrika | 2014年 / 77卷
关键词：
Sooner and later waiting times; Probability generating function ; Pattern; Double generating function; Multiple players problem; Polya urn model; Primary 60E05; Secondary 60J10;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this article, we study sooner/later waiting time problems for simple patterns in a sequence of bivariate trials. The double generating functions of the sooner/later waiting times for the simple patterns are expressed in terms of the double generating functions of the numbers of occurrences of the simple patterns. Effective computational tools are developed for the evaluation of the waiting time distributions along with some examples. The results presented here provide perspectives on the waiting time problems arising from bivariate trials and extend a framework for studying the exact distributions of patterns. Finally, some examples are given in order to illustrate how our theoretical results are employed for the investigation of the waiting time problems for simple patterns.
引用
收藏
页码：895 / 920
页数：25
相关论文
共 37 条
[1]  
Aki S(1999)Sooner and later waiting time problems for runs in Markov dependent bivariate trials Ann Inst Stat Math 51 17-29
[2]  
Hirano K(2001)Waiting times for patterns in a sequence of multistate trials J Appl Probab 38 508-518
[3]  
Antzoulakos DL(2001)Distributions of numbers of success runs of fixed length in Markov dependent trials Ann Inst Stat Math 53 599-619
[4]  
Antzoulakos DL(1990)Sooner and later waiting time problems for Bernoulli trials: frequency and run quotas Stat Probab Lett 9 5-11
[5]  
Chadjiconstantinidis S(2007)Success runs in a sequence of exchangeable binary trials J Stat Plan Inference 137 2954-2963
[6]  
Ebneshahrashoob M(1996)Distribution theory of runs and patterns associated with a sequence of multi-state trials Stat Sinica 6 957-974
[7]  
Sobel M(2003)On ordered series and later waiting time distributions ina sequence of Markov dependent multistate trials J Appl Probab 40 623-642
[8]  
Eryilmaz S(2008)Methods for studying generalized birthday and coupon collection problems Commun Stat Simul Comput 37 844-862
[9]  
Demir S(2009)On waiting time distributions associated with compound patterns in a sequence of multi-state trials Ann Inst Stat Math 61 499-516
[10]  
Fu JC(2011)Distributions of simple patterns in some kinds of exchangeable sequence J Stat Plan Inference 141 2532-2544
1234