A Generalization of the Mejzler--de Haan Theorem

摘要

Let (k_n) be a sequence of positive integers such that k_no infty as noinfty. Let X^st_{n1}, ldots,X^st_{nk_n}, nin{f N}, be a double array of random variables such that for each n the random variables X^st_{n1},ldots, X^st_{nk_n} are independent with a common distribution function F_n, and let us denote M^st_n=max{X^st_{n1},dots,X^st_{nk_n}}. We consider an example of double array random variables connected with a certain combinatorial waiting time problem (including both dependent and independent cases), where k_n=n for all n and the limiting distribution function for M^st_n is Lambda(x)=exp(-e^{-x}), although none of the distribution functions F_n belongs to the domain of attraction