Spacings around an order statistic

作者：Nagaraja H N^*; Bharath Karthik; Zhang Fangyuan

来源：Annals of the Institute of Statistical Mathematics, 2015, 67(3): 515-540.

DOI：10.1007/s10463-014-0466-9

• Spacings
• Uniform distribution
• Central order statistics
• Intermediate order statistics
• Extremes
• Poisson process

We determine the joint limiting distribution of adjacent spacings around a central, intermediate, or an extreme order statistic of a random sample of size from a continuous distribution . For central and intermediate cases, normalized spacings in the left and right neighborhoods are asymptotically i.i.d. exponential random variables. The associated independent Poisson arrival processes are independent of . For an extreme , the asymptotic independence property of spacings fails for in the domain of attraction of Fr,chet and Weibull () distributions. This work also provides additional insight into the limiting distribution for the number of observations around for all three cases.

• 出版日期2015-6