ON INDEPENDENCE OF k-RECORD PROCESSES: IGNATOV'S THEOREM REVISITED
成果类型：
Article
署名作者：
Yao, Yi-Ching
署名单位：
Academia Sinica - Taiwan; Colorado State University System; Colorado State University Fort Collins
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
发表日期：
1997
页码：
815-821
关键词：
摘要：
For an infinite sequence of independent and identically distributed (i.i.d.) random variables, the k-record process consists of those terms that are the kth largest at their appearance. Ignatov's theorem states that the k-record processes, k = 1, 2,..., are i.i.d. A new proof is given which is based on a continualization'' argument. An advantage of this fairly simple approach is that Ignatov's theorem can be stated in a more general form by allowing for different tiebreaking rules. In particular, three tiebreakers are considered and shown to be related to Bernoulli, geometric and Poisson distributions.