Gaussian limits associated with the Poisson-Dirichlet distribution and the Ewens sampling formula

DOI10.1214/aoap/1015961157zbMath1010.62101OpenAlexW2161014486MaRDI QIDQ1872418

Paul Joyce, Stephen M. Krone, Thomas G. Kurtz

Publication date: 6 May 2003

Published in: The Annals of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aoap/1015961157

Mathematics Subject Classification ID

Asymptotic distribution theory in statistics (62E20) Applications of statistics to biology and medical sciences; meta analysis (62P10) Central limit and other weak theorems (60F05) Problems related to evolution (92D15)

Related Items (15)

When can one detect overdominant selection in the infinite-alleles model? ⋮ Asymptotic Behaviour of Poisson-Dirichlet Distribution and Random Energy Model ⋮ On sampling distributions for coalescent processes with simultaneous multiple collisions ⋮ A Central Limit Theorem Associated with the Transformed Two-Parameter Poisson–Dirichlet Distribution ⋮ The two-parameter Poisson-Dirichlet point process ⋮ Large deviations associated with Poisson-Dirichlet distribution and Ewens sampling formula ⋮ Moderate deviations for Poisson-Dirichlet distribution ⋮ Estimating the large mutation parameter of the Ewens sampling formula ⋮ Paul Joyce and the infinite alleles model ⋮ Simulating the component counts of combinatorial structures ⋮ Diffusion processes and the Ewens sampling formula ⋮ Asymptotic behavior of the Poisson-Dirichlet distribution for large mutation rate ⋮ Poisson-Dirichlet distribution with small mutation rate ⋮ Limit theorems associated with the Pitman–Yor process ⋮ The sampling formula and Laplace transform associated with the two-parameter Poisson-Dirichlet distribution

Cites Work

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• Continuity and weak convergence of ranked and size-biased permutations on the infinite simplex
• The population structure associated with the Ewens sampling formula
• On the distribution of allele frequencies in a diffusion model
• Weak limit theorems for stochastic integrals and stochastic differential equations
• Is the most frequent allele the oldest?
• The role of population size in molecular evolution
• Convergence to Fleming-Viot processes in the weak atomic topology
• Partition structures and sufficient statistics

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