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Some comments on “The density flatness phenomenon” by Alhakim and Molchanov and the Dickman distribution

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  • Weissman, Ishay

Abstract

In a recent paper by Alhakim and Molchanov (2019), the authors deal with a certain sum of independent and identically distributed random variables and with its limiting distribution. The authors derive very interesting properties of the limiting distribution, unaware of the fact that it has been previously studied and referred to in the literature as the Dickman distribution. In this letter we compare the results to existing literature and make some historical notes. At the end we derive some extensions to Alhakim and Molchanov’s results.

Suggested Citation

  • Weissman, Ishay, 2023. "Some comments on “The density flatness phenomenon” by Alhakim and Molchanov and the Dickman distribution," Statistics & Probability Letters, Elsevier, vol. 194(C).
    • Handle: RePEc:eee:stapro:v:194:y:2023:i:c:s0167715222002541
    DOI: 10.1016/j.spl.2022.109741
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    References listed on IDEAS

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    1. Weissman, Ishay, 2017. "Sum of squares of uniform random variables," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 147-154.
    2. Alhakim, Abbas & Molchanov, S., 2019. "The density flatness phenomenon," Statistics & Probability Letters, Elsevier, vol. 152(C), pages 156-161.
    3. Devroye, Luc & Fawzi, Omar, 2010. "Simulating the Dickman distribution," Statistics & Probability Letters, Elsevier, vol. 80(3-4), pages 242-247, February.
    Full references (including those not matched with items on IDEAS)

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