On the asymptotic distribution of the discrete scan statistic
| Autor: | Markos V. Koutras, Michael V. Boutsikas |
|---|---|
| Rok vydání: | 2006 |
| Předmět: |
Statistics and Probability
Discrete mathematics Extreme value theorem Scan statistic General Mathematics 010102 general mathematics Asymptotic distribution Poisson distribution 01 natural sciences 010104 statistics & probability symbols.namesake Statistics symbols Probability distribution 0101 mathematics Statistics Probability and Uncertainty Completeness (statistics) Statistic Statistical hypothesis testing Mathematics |
| Zdroj: | Journal of Applied Probability. 43:1137-1154 |
| ISSN: | 1475-6072 0021-9002 |
| Popis: | The discrete scan statistic in a binary (0-1) sequence of n trials is defined as the maximum number of successes within any k consecutive trials (n and k, n ≥ k, being two positive integers). It has been used in many areas of science (quality control, molecular biology, psychology, etc.) to test the null hypothesis of uniformity against a clustering alternative. In this article we provide a compound Poisson approximation and subsequently use it to establish asymptotic results for the distribution of the discrete scan statistic as n, k → ∞ and the success probability of the trials is kept fixed. An extreme value theorem is also provided for the celebrated Erdős-Rényi statistic. |
| Databáze: | OpenAIRE |
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