Spacings around and order statistic

Nagaraja, H. N. and Bharath, Karthik and Zhang, Fangyuan (2015) Spacings around and order statistic. Annals of the Institute of Statistical Mathematics, 67 (3). pp. 515-540. ISSN 1572-9052

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Abstract

We determine the joint limiting distribution of adjacent spacings around a central, intermediate, or an extreme order statistic Xk:n of a random sample of size n from a continuous distribution 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 Xk:n. For an extreme Xk:n, the asymptotic independence property of spacings fails for F in the domain of attraction of Fréchet and Weibull (α≠1) distributions. This work also provides additional insight into the limiting distribution for the number of observations around Xk:n for all three cases.

Item Type: Article
RIS ID: https://nottingham-repository.worktribe.com/output/753476
Additional Information: The final publication is available at Springer via http://dx.doi.org/10.1007/s10463-014-0466-9.
Keywords: Spacings; uniform distribution; central order statistics; intermediate order statistics; extremes; Poisson process.
Schools/Departments: University of Nottingham, UK > Faculty of Science > School of Mathematical Sciences
Identification Number: https://doi.org/10.1007/s10463-014-0466-9
Depositing User: Bharath, Karthik
Date Deposited: 19 Jun 2017 13:19
Last Modified: 04 May 2020 17:09
URI: http://eprints.nottingham.ac.uk/id/eprint/43597

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