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Journal of the London Mathematical Society 1979 s2-19(1):170-174; doi:10.1112/jlms/s2-19.1.170
© 1979 by London Mathematical Society
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© Oxford University Press

A Note on a Paper of Barnes and Tucker

Peter Hall

Department of Statistics, S.G.S. Australian National University P.O. Box 4, Canberra, A.C.T. 2600, Australia

Let X1, X2, X3, ... be independent and identically distributed random variables and let Xnr denote the r'th largest of {X1, X2, ..., Xn), 1 ≤ r ≤ n. In a recent paper in this Journal, Barnes and Tucker examined conditions under which Xn1/b(n) -> c in probability or with probability one, where c and b(n), n ≥ 1, are constants. In this note we continue their examination and study the convergence of Xnr/b(n), r ≥ 1, to c. We improve on Barnes and Tucker's results in the case r = 1.


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