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https://hdl.handle.net/20.500.14365/2280
Title: | Discrete Scan Statistics Generated by Exchangeable Binary Trials |
Authors: | Eryılmaz, Serkan |
Keywords: | Bernoulli sequence exchangeable binary trial reliability scan statistics Coherent Systems Success Runs Urn Model Reliability Distributions Sequences |
Publisher: | Cambridge Univ Press |
Abstract: | Let {X-i}(i=1)(n) be a sequence of random variables with two possible outcomes, denoted 0 and 1. Define a random variable S-n,S-m to be the maximum number of Is within any m consecutive trials in {X-i}(i=1)(n). The random variable S-n,S-m is called a discrete scan statistic and has applications in many areas. In this paper we evaluate the distribution of discrete scan statistics when {X-i}(i=1)(n) consists of exchangeable binary trials. We provide simple closed-form expressions for both conditional and unconditional distributions of S-n,S-m for 2m >= n. These results are also new for independent, identically distributed Bernoulli trials, which are a special case of exchangeable trials. |
URI: | https://doi.org/10.1239/jap/1294170521 https://hdl.handle.net/20.500.14365/2280 |
ISSN: | 0021-9002 1475-6072 |
Appears in Collections: | Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection |
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