Characterization of tail distributions based on record values by using the Beurling's Tauberian theorem

In this paper, we mainly investigate the converse of a well-known theorem proved by Shorrock (J. Appl. Prob. 9, 316-326 1972b), which states that the regular variation of tail distribution implies a non-degenerate limit for the ratios of the record values. Specifically, the converse is proved by using Beurling extension of Wiener's Tauberian theorem. This equivalence is extended to the Weibull and Gumbel max-domains of attraction.