Abstract
In this paper, the joint distribution of some special linear combinations of the (internally) studentized order statistics are derived for both normal and exponential populations; the exact relationship between their pdf's is also obtained. The exact sampling distributions of studentized extreme deviation statistic, which has been proposed by Pearson and Chandra Sekar (1936,Biometrika,28, 308–320), are derived for these two populations. An application to the most powerful location and scale invariant test is discussed briefly.
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Hwang, TY., Hu, CY. On the joint distribution of studentized order statistics. Ann Inst Stat Math 46, 165–177 (1994). https://doi.org/10.1007/BF00773601
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DOI: https://doi.org/10.1007/BF00773601