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The asymptotic distribution of numbers of observations near order statistics |
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| Authors: | Anna Dembi&#x;ska N Balakrishnan |
| Institution: | aFaculty of Mathematics and Information Science, Warsaw University of Technology, Pl. Politechniki 1, 00-661 Warsaw, Poland bDepartment of Mathematics and Statistics, McMaster University, 1280 Main Street West, Hamilton, Ont., Canada L8S 4K1 |
| Abstract: | In this paper, we discuss the limiting behavior of numbers of observations near an order statistic. We then derive an expression for the joint distribution of the numbers of observations that fall into the open right a-vicinity and left b-vicinity of k th and (n-r)th order statistics, respectively, from a sample of size n and establish the result that they are asymptotically independent under suitable conditions. |
| Keywords: | Order statistics Near order statistic observations Limit theorems Asymptotic independence |
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