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Moments do not determine tail

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  • Chao, Min-Te
  • Liang, Wen-Qi

Abstract

It is an elementary fact that the existence of moments are determined by the tail behavior of the distribution. The converse, however, needs to be discussed. We provide an elementary example that shows random variables with only a few finite moments may have a p.d.f. [latin small letter f with hook](x)[downwards arrow]0 such that as x --> [infinity], lim inf xb[latin small letter f with hook](x) = 0 for all b> 0.

Suggested Citation

  • Chao, Min-Te & Liang, Wen-Qi, 1994. "Moments do not determine tail," Statistics & Probability Letters, Elsevier, vol. 19(4), pages 327-328, March.
    • Handle: RePEc:eee:stapro:v:19:y:1994:i:4:p:327-328
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    Keywords

    Regularly varying function;

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