Spacings around and order statistic
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 asymptot...
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| Format: | Article |
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Springer
2015
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| Online Access: | https://eprints.nottingham.ac.uk/43597/ |
| _version_ | 1848796724639825920 |
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| author | Nagaraja, H. N. Bharath, Karthik Zhang, Fangyuan |
| author_facet | Nagaraja, H. N. Bharath, Karthik Zhang, Fangyuan |
| author_sort | Nagaraja, H. N. |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T19:52:32Z |
| format | Article |
| id | nottingham-43597 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:52:32Z |
| publishDate | 2015 |
| publisher | Springer |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-435972020-05-04T17:09:42Z https://eprints.nottingham.ac.uk/43597/ Spacings around and order statistic Nagaraja, H. N. Bharath, Karthik Zhang, Fangyuan 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. Springer 2015-06-30 Article PeerReviewed Nagaraja, H. N., 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 Spacings; uniform distribution; central order statistics; intermediate order statistics; extremes; Poisson process. https://link.springer.com/article/10.1007%2Fs10463-014-0466-9 doi:10.1007/s10463-014-0466-9 doi:10.1007/s10463-014-0466-9 |
| spellingShingle | Spacings; uniform distribution; central order statistics; intermediate order statistics; extremes; Poisson process. Nagaraja, H. N. Bharath, Karthik Zhang, Fangyuan Spacings around and order statistic |
| title | Spacings around and order statistic |
| title_full | Spacings around and order statistic |
| title_fullStr | Spacings around and order statistic |
| title_full_unstemmed | Spacings around and order statistic |
| title_short | Spacings around and order statistic |
| title_sort | spacings around and order statistic |
| topic | Spacings; uniform distribution; central order statistics; intermediate order statistics; extremes; Poisson process. |
| url | https://eprints.nottingham.ac.uk/43597/ https://eprints.nottingham.ac.uk/43597/ https://eprints.nottingham.ac.uk/43597/ |