Immigrated urn models - asymptotic properties and applications

Urn models have been widely studied and applied in both scientific and social disciplines. In clinical studies, the adoption of urn models in treatment allocation schemes has been proved to be beneficial to both researchers, by providing more efficient clinical trials, and patients, by increasing the probability of receiving the better treatment. In this paper, we endeavor to derive a very general class of immigrated urn models that incorporates the immigration mechanism into the urn process. Important asymptotic properties are developed and illustrative examples are provided to demonstrate the applicability of our proposed class of urn models. In general, the immigrated urn model has smaller variability than the corresponding urn model. Therefore, it is more powerful when used in clinical trials.