MAXIMA OF POISSON-LIKE VARIABLES AND RELATED TRIANGULAR ARRAYS

• 成果类型: Article
• 署名作者: Anderson, Clive W.; Coles, Stuart G.; Husler, Jurg
• 署名单位: University of Sheffield; Lancaster University; University of Bern
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/aoap/1043862420
• 发表日期: 1997
• 页码: 953-971
• 关键词: integral limit-theorems; large deviations; cramers condition; account

摘要

It is known that maxima of independent Poisson variables cannot be normalized to converge to a nondegenerate limit distribution. On the other hand, the Normal distribution approximates the Poisson distribution for large values of the Poisson mean, and maxima of random samples of Normal variables may be linearly scaled to converge to a classical extreme value distribution. We here explore the boundary between these two kinds of behavior. Motivation comes from the wish to construct models for the statistical analysis of extremes of background gamma radiation over the United Kingdom. The methods extend to row-wise maxima of certain triangular arrays, for which limiting distributions are also derived.