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- W2088694545 abstract "Let $(k_n)$ be a sequence of positive integers such that $k_nto infty$ as $ntoinfty$. Let $X^ast_{n1}, ldots,X^ast_{nk_n}$, $nin{bf N}$, be a double array of random variables such that for each n the random variables $X^ast_{n1},ldots, X^ast_{nk_n}$ are independent with a common distribution function $F_n$, and let us denote $M^ast_n=max{X^ast_{n1},dots,X^ast_{nk_n}}$. 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 $M^ast_n$ is $Lambda(x)=exp(-e^{-x})$, although none of the distribution functions $F_n$ belongs to the domain of attraction $D(Lambda)$. We also generalize the Mejzler--de Haan theorem and give the necessary and sufficient conditions for the sequence $(F_n)$ under which there exist sequences $a_n>0$ and $b_nin {bf R}$, $nin{bf N}$, such that $F_n^{k_n}(a_nx+b_n)toexp(-e^{-x})$ as $ntoinfty$ for every real x." @default.
- W2088694545 created "2016-06-24" @default.
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- W2088694545 date "2006-01-01" @default.
- W2088694545 modified "2023-10-14" @default.
- W2088694545 title "A Generalization of the Mejzler--de Haan Theorem" @default.
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- W2088694545 doi "https://doi.org/10.1137/s0040585x97981561" @default.
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