Discrete Scan Statistics Generated by Exchangeable Binary Trials
2010 ◽
Vol 47
(04)
◽
pp. 1084-1092
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Keyword(s):
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,m to be the maximum number of 1s within any m consecutive trials in {X i } i=1 n . The random variable S n,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,m for 2m ≥ n. These results are also new for independent, identically distributed Bernoulli trials, which are a special case of exchangeable trials.
2010 ◽
Vol 47
(4)
◽
pp. 1084-1092
◽
2021 ◽
Vol 73
(1)
◽
pp. 62-67
2012 ◽
Vol 49
(4)
◽
pp. 1188-1193
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Keyword(s):
2004 ◽
Vol 41
(4)
◽
pp. 1081-1092
◽
2009 ◽
Vol 41
(01)
◽
pp. 13-37
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2012 ◽
Vol 49
(01)
◽
pp. 199-209
◽