On a Two-Parameter Yule-Simon Distribution

Baur, Erich; Bertoin, Jean (2021). On a Two-Parameter Yule-Simon Distribution In: A Lifetime of Excursions Through Random Walks and Lévy Processes. Progress in Probability: Vol. 1 (pp. 59-82). Cham, Switzerland: Springer https://doi.org/10.1007/978-3-030-83309-1

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We extend the classical one-parameter Yule-Simon law to a version depending on two parameters, which in part appeared in Bertoin (J Stat Phys 176(3):679–691, 2019) in the context of a preferential attachment algorithm with fading memory. By making the link to a general branching process with age- dependent reproduction rate, we study the tail-asymptotic behavior of the two- parameter Yule-Simon law, as it was already initiated in Bertoin (J Stat Phys 176(3):679–691, 2019). Finally, by superposing mutations to the branching process, we propose a model which leads to the two-parameter range of the Yule-Simon law, generalizing thereby the work of Simon (Biometrika 42(3/4):425–440, 1955) on limiting word frequencies.

Item Type:	Book Section (Book Chapter)
Division/Institute:	School of Engineering and Computer Science > Institut für Optimierung und Datenanalyse IODA
Name:	Baur, Erich and Bertoin, Jean
Subjects:	Q Science > QA Mathematics
ISSN:	1050-6977
ISBN:	978-3-030-83308-4
Series:	Progress in Probability
Publisher:	Springer
Language:	English
Submitter:	Erich Baur
Date Deposited:	14 Jan 2022 11:13
Last Modified:	14 Jan 2022 11:13
Publisher DOI:	https://doi.org/10.1007/978-3-030-83309-1
Uncontrolled Keywords:	Fluctuation Theory, Lévy Processes, Random Walks, Ron Doney, Probability, Diffusions
ARBOR DOI:	10.24451/arbor.16422
URI:	https://arbor.bfh.ch/id/eprint/16422