On waiting time distribution of runs of ones or zeros in a Bernoulli sequence

被引：4

作者：

Kim, Sungsu ^{[1
]}

Park, Chongjin ^{[2
]}

Oh, Jungtaek ^{[3
]}

机构：

[1] Keimyung Univ, Dept Gen Educ, Taegu, South Korea

[2] San Diego State Univ, Dept Math & Stat, San Diego, CA 92182 USA

[3] Kyungpook Natl Univ, Dept Math, Taegu, South Korea

来源：

STATISTICS & PROBABILITY LETTERS | 2013年 / 83卷 / 01期

关键词：

Bernoulli sequences; Fibonacci sequences; Probability distribution function; Probability generating function; Sooner waiting time; SOONER; TRIALS; SUCCESS;

D O I：

10.1016/j.spl.2012.10.001

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：

Consider an infinite sequence of Bernoulli trials {X-i vertical bar i = 1, 2, ...}. Let W(k) denote the waiting time, the number of trials needed, to get either consecutive k ones or k zeros for the first time. The probability distribution of W(k) is derived for both independent and homogeneous two-state Markovian Bernoulli trials, using a generalized Fibonacci sequence of order k. For independent Bernoulli trials, a special case of symmetric trial with p = 1/2 is considered. (C) 2012 Elsevier B.V. All rights reserved.

引用

页码：339 / 344

页数：6

共 14 条

[1] Sooner and later waiting time problems for success and failure runs in higher order Markov dependent trials [J].