Distributions in the constant-differentials P\'olya process
Statistics Theory
2018-08-28 v2 Statistics Theory
Abstract
We study a class of unbalanced constant-differentials P\'olya processes on white and blue balls. We show that the number of white balls, the number of blue balls, and the total number of balls, when appropriately scaled, all converge in distribution to a gamma random variables with parameters depending on the differential index and the amount of ball addition at the epochs, but not on the initial conditions. The result is obtained by an analytic approach utilizing partial differential equations.
Cite
@article{arxiv.1806.04303,
title = {Distributions in the constant-differentials P\'olya process},
author = {Hosam M. Mahmoud and Panpan Zhang},
journal= {arXiv preprint arXiv:1806.04303},
year = {2018}
}