 Spacings around an order statisticH. Nagaraja (), Karthik Bharath () and Fangyuan Zhang () Annals of the Institute of Statistical Mathematics, 2015, vol. 67, issue 3, 515-540 Abstract: We determine the joint limiting distribution of adjacent spacings around a central, intermediate, or an extreme order statistic $$X_{k:n}$$ X k : n of a random sample of size $$n$$ n from a continuous distribution $$F$$ F . 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 $$X_{k:n}$$ X k : n . For an extreme $$X_{k:n}$$ X k : n , the asymptotic independence property of spacings fails for $$F$$ F in the domain of attraction of Fréchet and Weibull ( $$\alpha \ne 1$$ α ≠ 1 ) distributions. This work also provides additional insight into the limiting distribution for the number of observations around $$X_{k:n}$$ X k : n for all three cases. Copyright The Institute of Statistical Mathematics, Tokyo 2015 Keywords: Spacings; Uniform distribution; Central order statistics; Intermediate order statistics; Extremes; Poisson process (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:spr:aistmt:v:67:y:2015:i:3:p:515-540 Ordering information: This journal article can be ordered from DOI: 10.1007/s10463-014-0466-9 Access Statistics for this article Annals of the Institute of Statistical Mathematics is currently edited by Tomoyuki Higuchi More articles in Annals of the Institute of Statistical Mathematics from Springer, The Institute of Statistical Mathematics |
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