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On a certain class of infinitely divisible distributions

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Abstract

We characterize the class of distribution functions Φ(x), which are limits in the following sense: there exist a sequence of independent and equally distributed random variables {ξ n }, numerical sequences {a k }, {b k } and natural numbers {n k } such that

$$\mathop {lim}\limits_{k \to \infty } Prob\left\{ {\frac{1}{{a_k }}\mathop {\Sigma }\limits_{k = 1}^{n_k } \xi _k - b_k< x} \right\} = \Phi (x)$$

and

$$\mathop {\lim \inf }\limits_{k \to \infty } (n_k /n_{k + 1} ) > 0$$

.

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Authors and Affiliations

  1. Institute of Mathematics and Department of Statistics, The Hebrew University of Jerusalem, Jerusalem, Israel

    D. Mejzler

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  1. D. Mejzler
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Mejzler, D. On a certain class of infinitely divisible distributions. Israel J. Math. 16, 1–19 (1973). https://doi.org/10.1007/BF02761966

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  • DOI: https://doi.org/10.1007/BF02761966

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