Generalized gamma approximation with rates for urns, walks and trees

@article{Pekoz2016GeneralizedGA,
  title={Generalized gamma approximation with rates for urns, walks and trees},
  author={Erol A. Pekoz and Adrian R{\"o}llin and Nathan Ross},
  journal={Annals of Probability},
  year={2016},
  volume={44},
  pages={1776-1816}
}
We study a new class of time inhomogeneous Polya-type urn schemes and give optimal rates of convergence for the distribution of the properly scaled number of balls of a given color to nearly the full class of generalized gamma distributions with integer parameters, a class which includes the Rayleigh, half-normal and gamma distributions. Our main tool is Stein’s method combined with characterizing the generalized gamma limiting distributions as fixed points of distributional transformations… 

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