On reinforcement-depletion compartmental urn models
Donnelly P., Whitt W.
<jats:p>We verify and extend a conjecture of Purdue (1981) concerning the stochastic monotonicity of absorption times in a class of compartmental urn models. We also describe the effect of increased variability in the reinforcement sizes. Finally, we investigate variability in the content process for large populations. In many applications, compartmental models substantially under-represent the variability observed in the data, so that there has been considerable interest in modifying the model to increase the variability. We show that the squared coefficient of variation of the content is not asymptotically negligible when both the size and the variability of the reinforcements are of the same order as the initial population.</jats:p>