Gaussian Limits Associated with the Poisson-Dirichlet Distribution and the Ewens Sampling Formula
نویسندگان
چکیده
منابع مشابه
Large Deviations Associated with Poisson–dirichlet Distribution and Ewens Sampling Formula
Several results of large deviations are obtained for distributions that are associated with the Poisson–Dirichlet distribution and the Ewens sampling formula when the parameter θ approaches infinity. The motivation for these results comes from a desire of understanding the exact meaning of θ going to infinity. In terms of the law of large numbers and the central limit theorem, the limiting proc...
متن کاملThe ubiquitous Ewens sampling formula
Ewens’s sampling formula exemplifies the harmony of mathematical theory, statistical application, and scientific discovery. The formula not only contributes to the foundations of evolutionary molecular genetics, the neutral theory of biodiversity, Bayesian nonparametrics, combinatorial stochastic processes, and inductive inference but also emerges from fundamental concepts in probability theory...
متن کاملRejoinder: The Ubiquitous Ewens Sampling Formula
The main article and extended discussion point to Ewens’s sampling formula (ESF) as one of a few essential probability distributions. Arratia, Barbour and Tavaré explain the emergence of ESF by the Feller coupling and also touch on number theoretic considerations; Feng provides deeper background on diffusion processes and nonequilibrium versions of ESF; and McCullagh regales us with a story fro...
متن کاملConvergence Time to the Ewens Sampling Formula
In this paper, we establish the cutoff phenomena for the discrete time infinite alleles Moran model. If M is the population size and μ is the mutation rate, we find a cutoff time of log(Mμ)/μ generations. The stationary distribution for this process in the case of sampling without replacement is the Ewens sampling formula. We show that the bound for the total variation distance from the generat...
متن کاملA finitary characterization of Ewens sampling formula
The clustering of agents in the market is a typical problem dealt with by the new approaches to macroeconomic modeling, that describe macroscopic variables in terms of the behavior of a large collection of microeconomic entities. Clustering has a lot of economical interpretations [3], that are often described by Ewens Sampling Formula (ESF). This formula can be traced back to Fisher as “species...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Annals of Applied Probability
سال: 2002
ISSN: 1050-5164
DOI: 10.1214/aoap/1015961157