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SUMMARY:Ross Maller (ANU)
DTSTART:20201001T070000Z
DTEND:20201001T080000Z
DTSTAMP:20260423T035959Z
UID:PVSeminar/3
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/PVSeminar/3/
 ">A Generalized Dickman Distribution and the Number of Species in a Negati
 ve Binomial Process Model</a>\nby Ross Maller (ANU) as part of Probability
  Victoria Seminar (PVSeminar)\n\n\nAbstract\nIn Ipsen\, Maller\, Shemehsav
 ar (J. Theoret. Prob.\, 2019) we defined a new class of distributions rela
 ted to Kingman’s PD$_\\alpha $ distribution\, which we called PD$_\\alph
 a ^{(r)}$. It has two parameters\, $\\alpha\\in (0\,1)$ and $r > 0.$\n\nA 
 version of Ewens’ sampling formula was derived for it\, and we obtained 
 a formula for the probability mass function of Kn\, the number of allele t
 ypes/species observed in a sample of size n from PD$_\\alpha ^{(r)}$.\n\nT
 he aim of this seminar is to sketch a derivation of the large-sample distr
 ibution of $K_n$ as $n \\to\\infty$.\n\nWe cite a set of genetics data on 
 the near-threatened marsupial quoll as a nice motivation. [Joint work with
  Yuguang Ipsen and Soudabeh Shemehsavar.]\n
LOCATION:https://researchseminars.org/talk/PVSeminar/3/
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