DISCRETE SCAN STATISTICS GENERATED BY EXCHANGEABLE BINARY TRIALS

作者：Eryilmaz Serkan^*

来源：Journal of Applied Probability, 2010, 47(4): 1084-1092.

DOI：10.1239/jap/1294170521

• Bernoulli sequence
• exchangeable binary trial
• reliability
• scan statistics

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 Is 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.

• 出版日期2010-12