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<p>The probabilistic Dickman law, defined by the known Dickman function, and its generalized versions are considered. In the paper, we obtain a general criterion of the weak convergence to these laws for the distributions of sums of independent nonnegative random variables within the series scheme in the classical setting. Moreover, we obtain a special criterion of the convergence for the case where the summing random variables have finite expectations. Bibliography: 13 titles.</p>

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SUMS OF INDEPENDENT RANDOM VARIABLES AND THE GENERALIZED DICKMAN LAWS

  • 期刊论文

  • 发表日期：

    2025年9月1日

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  • K. A. Tregubova,
  • A. A. Khartov

摘要

The probabilistic Dickman law, defined by the known Dickman function, and its generalized versions are considered. In the paper, we obtain a general criterion of the weak convergence to these laws for the distributions of sums of independent nonnegative random variables within the series scheme in the classical setting. Moreover, we obtain a special criterion of the convergence for the case where the summing random variables have finite expectations. Bibliography: 13 titles.