Moments do not determine tail

Min-Te Chao and Wen-Qi Liang

Statistics & Probability Letters, 1994, vol. 19, issue 4, 327-328

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.

Keywords: Regularly; varying; function (search for similar items in EconPapers)
Date: 1994
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