Shortest and longest length of success runs in binary sequences

被引：30

作者：

Makri, Frosso S. ^{[1
]}

Philippou, Andreas N.

Psillakis, Zaharias M.

机构：

[1] Univ Patras, Dept Math, GR-26110 Patras, Greece

[2] Univ Patras, Dept Phys, GR-26110 Patras, Greece

来源：

JOURNAL OF STATISTICAL PLANNING AND INFERENCE | 2007年 / 137卷 / 07期

关键词：

Bernoulli trials; Polya-Eggenberger sampling scheme; success runs; linear and circular binary sequences; reliability of consecutive systems;

D O I：

10.1016/j.jspi.2006.07.007

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：

The shortest and the longest length of success runs statistics in binary sequences are considered. The sequences are arranged on a line or on a circle. Exact probabilities of these statistics are derived, both in closed formulae via combinatorial analysis, as well as recursively. Furthermore, their joint probability distribution function and cumulative distribution function are obtained. The results are developed first for Bernoulli trials (i.i.d. binary sequences), and then they are generalized to the Polya-Eggenberger sampling scheme. For the latter case, the length of the longest success run is related to other success runs statistics and to reliability of consecutive systems. (c) 2006 Elsevier B.V. All rights reserved.

引用

页码：2226 / 2239

页数：14

共 21 条

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