On reinforcement-depletion compartmental urn models

The authors verify and extend a conjecture of Purdue concerning the stochastic monotonicity of absorption times in a class of compartmental urn models. They also describe the effect of increased variability in the reinforcement sizes. Finally, the authors 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. The authors 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.