Hostname: page-component-77c89778f8-gvh9x Total loading time: 0 Render date: 2024-07-20T07:10:54.910Z Has data issue: false hasContentIssue false
  • English
  • Français

Size-biased filtering of Poisson–Dirichlet samples with an application to partition structures in genetics

Published online by Cambridge University Press:  24 August 2016

Fred M. Hoppe
Fred M. Hoppe*
Affiliation:
The University of Michigan, Ann Arbor
*
∗Postal address: Department of Statistics, 1444 Mason Hall, 419 South State Street, Ann Arbor, MI 48109–1027, USA.
Get access Rights & Permissions [Opens in a new window]

Abstract

A characteristic property of the Ewen sampling formula is shown to follow from the invariance under size-biased sampling of the Poisson–Dirichlet distribution.

Keywords

EWEN SAMPLING FORMULASIZE-BIASED SAMPLINGPOPULATION GENETICS
Type
Short Communications
Information
Journal of Applied Probability , Volume 23 , Issue 4 , December 1986 , pp. 1008 - 1012
Copyright
Copyright © Applied Probability Trust 1986 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Connor, R. J. and Mosimann, J. E. (1969) Concepts of independence for proportions with a generalization of the Dirichlet distribution. J. Amer. Statist. Assoc. 64, 194–206.Google Scholar
Engen, S. (1975) A note on the geometric series as a species frequency model. Biometrika 62, 694–699.Google Scholar
Ewens, W. J. (1972) The sampling theory of selectively neutral alleles. Theoret. Popn Biol. 3, 87–112.Google Scholar
Fabius, J. (1973) Two characterizations of the Dirichlet distribution. Ann. Statist. 1, 583–587.Google Scholar
James, I. R. and Mosimann, J. E. (1980) A new characterization of the Dirichlet distribution through neutrality. Ann. Statist. 8, 183–189.Google Scholar
Kingman, J. F. C. (1975) Random discrete distributions, J.R. Statist. Soc. B 37, 1–22.Google Scholar
Kingman, J. F. C. (1978) Random partitions in population genetics. Proc. R. Soc. London A 361, 1–20.Google Scholar
Mccloskey, J. W. (1965) A Model for the Distribution of Individuals by Species in an Environment. , Michigan State University.Google Scholar
Patil, G. P. and Taillie, C. (1977) Diversity as a concept and its implications for random communities. Bull. Internat. Statist. Inst. XLVII, 497–515.Google Scholar
Watterson, G. A. (1976) The stationary distribution of the infinitely-many neutral alleles diffusion model. J. Appl. Prob. 13, 639–651.Google Scholar