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

Ishay Weissman

Statistics & Probability Letters, 2023, vol. 194, issue C

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.

Keywords: Generalized Dickman distribution; Differential-delay equation; Perpetuity (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1016/j.spl.2022.109741

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