Strong laws for the k-th order statistic when k≦c log2 n

descriptionPublicationkeyboard_double_arrow_right Article 01 Apr 1986 English Publisher:Springer Science and Business Media LLCJournal:Probability Theory and Related Fields, volume 72, pages 133-154 (issn: 0178-8051, eissn: 1432-2064,

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Authors: Deheuvels, Paul;

doi: 10.1007/bf00343900

Strong laws for the k-th order statistic when k≦c log2 n

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Abstract

Let \(U_ 1,U_ 2,..\). be an i.i.d. sequence of random variables uniformly distributed over (0,1) and let for each n, \(U_{1,n}c_ n\quad i.o.)=0\) \((=1)\) and (ii) lower-lower class (upper-lower class) according as \(P(nU_{k_ n,n}

Related Organizations

University of Paris
France

Keywords

uniform distribution, Strong limit theorems, order statistics, upper and lower class sequences, Order statistics; empirical distribution functions, iterated logarithm laws, regularity conditions

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