Power limits for central order statistics: I. Continuous limit laws

详细信息    查看全文

• 作者：Guus Balkema ; Elisabeth Pancheva
• 关键词：Central order statistics ; Limit law ; Power transformations
• 刊名：Extremes
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：20
• 期：1
• 页码：91-110
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Statistics, general; Quality Control, Reliability, Safety and Risk; Civil Engineering; Hydrogeology; Environmental Management; Statistics for Business/Economics/Mathematical Finance/Insurance;
• 出版者：Springer US
• ISSN：1572-915X
• 卷排序：20

文摘

This paper lists the continuous limit distributions for central order statistics normalized by power transformations, and describes their domains of attraction. One may argue that power transformations are the natural normalizations to use if one wants to study the asymptotic behaviour of central order statistics. Power transformations preserve the origin, which may be assumed to be the quantile to which the order statistics converge. Our theory gives a nice extension of the theory developed by Smirnov more than sixty year ago. For the continuous power limits treated below the resemblance with the limit theory for extremes under linear transformations is striking.