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Generalizing a theorem of Katz

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  • Spataru, Aurel

Abstract

The Katz theorem states that if X1,X2,... are i.i.d. random variables, Sn=X1+...+Xn, n>=1, and t>=1, then [summation operator]n>=1nt-2P(Sn>=[epsilon]n) 0, if and only if EX1t =1nt-2P(Sn>=[epsilon]n), [epsilon]>0, when 1 =1, we show that one of these conditions is also necessary.

Suggested Citation

  • Spataru, Aurel, 2010. "Generalizing a theorem of Katz," Statistics & Probability Letters, Elsevier, vol. 80(13-14), pages 1136-1140, July.
    • Handle: RePEc:eee:stapro:v:80:y:2010:i:13-14:p:1136-1140
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