On characterizations of distributions via moments of record values (Q1073483)

Let \(\{X_ n\}^{\infty}_{n=1}\) be a sequence of i.i.d. random variables having continuous distribution F(x) with \(E| X|^{\ell +\epsilon}<\infty\) for some positive integer \(\ell\) and for some \(\epsilon >0.\) It is shown that for any fixed integer \(N\geq 0\) the sequence of moments of record values \(\{E(X_{L(n)})^{\ell}\}^{\infty}_{n=N}\) characterizes F. Furthermore, this result is applied to the weak convergence of continuous distributions.