Limiting distributions of extreme order statistics under power normalization and random index

作者：Peng Zuoxiang; Jiang Qin; Nadarajah Saralees^*

来源：Stochastics: An International Journal of Probability and Stochastic Processes , 2012, 84(4): 553-560.

DOI：10.1080/17442508.2011.573072

• limiting distribution
• order statistic
• power normalization
• random index
• shifted distribution

Let (X-n) be a sequence of independent and identically distributed random variables and let M-n((s)) denote the sth largest order statistic of X-k, 1 <= k <= n. In this note, the limiting distributions of M-Nn((s)) under power normalization are derived as the integer-valued random index N-n follows the shifted negative binomial, shifted Poisson and shifted binomial distributions.

• 出版日期2012
• 单位西南大学