Summary
Let {X n } =1∞ n be a sequence of i.i.d. random variables having continuous distribution F(x) with E|X| l+ε<∞ for some positive integer l and for some ε>0. It is shown that for any fixed integer N≧0 the sequence of moments of record values {E(X L(n) )l} ∞ n=N characterizes F. Furthermore, this result is applied to the weak convergence of continuous distributions.
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Lin, G.D. On characterizations of distributions via moments of record values. Probab. Th. Rel. Fields 74, 479–483 (1987). https://doi.org/10.1007/BF00363510
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DOI: https://doi.org/10.1007/BF00363510