Size biased sampling from the Dickman subordinator

Yuguang Ipsen; Ross Maller; Soudabeh Shemehsavar

doi:10.1016/j.spa.2020.07.002

Size biased sampling from the Dickman subordinator

Yuguang Ipsen, Ross Maller, Soudabeh Shemehsavar^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

The Dickman function and associated distribution play a prominent role in probabilistic number theory and in the theory of Poisson–Dirichlet distributions. These distributions in turn are closely related to properties of ordered jumps of subordinators. In the present paper we derive some remarkable invariance properties and other identities for the Dickman subordinator, related to the large jumps of the process. The implications of this for size-biased sampling from the Dickman distribution are drawn out.

Original language	English
Pages (from-to)	6880-6900
Number of pages	21
Journal	Stochastic Processes and their Applications
Volume	130
Issue number	11
DOIs	https://doi.org/10.1016/j.spa.2020.07.002
Publication status	Published - Nov 2020

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10.1016/j.spa.2020.07.002

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title = "Size biased sampling from the Dickman subordinator",

abstract = "The Dickman function and associated distribution play a prominent role in probabilistic number theory and in the theory of Poisson–Dirichlet distributions. These distributions in turn are closely related to properties of ordered jumps of subordinators. In the present paper we derive some remarkable invariance properties and other identities for the Dickman subordinator, related to the large jumps of the process. The implications of this for size-biased sampling from the Dickman distribution are drawn out.",

keywords = "Generalised Dickman distribution, Generalised Poisson–Dirichlet laws, Negative binomial point process, Size-biased sampling",

author = "Yuguang Ipsen and Ross Maller and Soudabeh Shemehsavar",

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year = "2020",

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doi = "10.1016/j.spa.2020.07.002",

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AU - Ipsen, Yuguang

AU - Maller, Ross

AU - Shemehsavar, Soudabeh

PY - 2020/11

Y1 - 2020/11

N2 - The Dickman function and associated distribution play a prominent role in probabilistic number theory and in the theory of Poisson–Dirichlet distributions. These distributions in turn are closely related to properties of ordered jumps of subordinators. In the present paper we derive some remarkable invariance properties and other identities for the Dickman subordinator, related to the large jumps of the process. The implications of this for size-biased sampling from the Dickman distribution are drawn out.

AB - The Dickman function and associated distribution play a prominent role in probabilistic number theory and in the theory of Poisson–Dirichlet distributions. These distributions in turn are closely related to properties of ordered jumps of subordinators. In the present paper we derive some remarkable invariance properties and other identities for the Dickman subordinator, related to the large jumps of the process. The implications of this for size-biased sampling from the Dickman distribution are drawn out.

KW - Generalised Dickman distribution

KW - Generalised Poisson–Dirichlet laws

KW - Negative binomial point process

KW - Size-biased sampling

UR - https://www.scopus.com/pages/publications/85088381373

U2 - 10.1016/j.spa.2020.07.002

DO - 10.1016/j.spa.2020.07.002

M3 - Article

SN - 0304-4149

VL - 130

SP - 6880

EP - 6900

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

IS - 11

ER -

Size biased sampling from the Dickman subordinator

Abstract

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