Complete stability of large order statistics |
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Authors: | Z F Li R J Tomkins |
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Institution: | (1) Department of Mathematics and Statistics, University of Regina, S4S 0A2, Saskatchewan, Canada |
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Abstract: | Fix an integerr1. For eachnr, letM
nr be the rth largest ofX
1,...,X
n, where {X
n,n1} is a sequence of i.i.d. random variables. Necessary and sufficient conditions are given for the convergence of
n=r
n
P|M
nr
/a
n
–1|<] for every >0, where {a
n} is a real sequence and –1. Moreover, it is shown that if this series converges for somer1 and some >–1, then it converges for everyr1 and every >–1. |
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Keywords: | Order statistics complete convergence -complete stability" target="_blank">gif" alt="agr" align="BASELINE" BORDER="0">-complete stability |
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