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Applied and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments.

4 votes
1 answer
792 views

Proof for power-law tail of Poisson-Dirichlet distribution (Pitman-Yor process & Zipf's law)

I'm trying to understand the motivation of using Pitman-Yor (PY) processes in language modeling, in particular Teh's hierarchical LM based on PY processes. A motivation frequently stated in research l …
Mirko Vogel's user avatar
4 votes
Accepted

Proof for power-law tail of Poisson-Dirichlet distribution (Pitman-Yor process & Zipf's law)

As an intermediate solution, I put up with the following proposition. It only gives the asymptotic behavior of the expectation of the stick-breaking weights while almost surely results exist, for sure …
Mirko Vogel's user avatar