TY - JOUR
T1 - Size biased sampling from the Dickman subordinator
AU - Ipsen, Yuguang
AU - Maller, Ross
AU - Shemehsavar, Soudabeh
N1 - Publisher Copyright:
© 2020 Elsevier B.V.
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 - http://www.scopus.com/inward/record.url?scp=85088381373&partnerID=8YFLogxK
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 -