Decision Sciences Seminar
Wednesday October 30, 2013
11:15AM - 12:30PM
Erol A. Peköz
Generalized gamma approximation with rates for urns, walk, and trees
We discuss a new class of time inhomogeneous Pólya-type urn schemes and give optimal rates of convergence for the distribution of the number of balls of a given color properly scaled) to nearly the full class of generalized gamma distributions, a class which includes the exponential, gamma, Rayleigh, chi, chi-squared, half-normal, and Weibull distributions. We then identify these urn models in recursive constructions of random walk paths which yields optimal rates of convergence for local time and height statistics of some random walk paths as well as for the size of some random subtrees of uniformly random binary trees and plane trees. The main tool is a new formulation of Stein's method for generalized gamma distributions which relies on characterizing these distributions as unique fixed points of certain distributional transformations reminiscent of the equilibrium distributional transformation from renewal theory.