  Urn models have been widely studied and applied in both scientific and social
science 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 likelihood of receiving the better treatment. In this paper, we
propose a new and general class of immigrated urn (IMU) models that
incorporates the immigration mechanism into the urn process. Theoretical
properties are developed and the advantages of the IMU models are discussed. In
general, the IMU models have smaller variabilities than the classical urn
models, yielding more powerful statistical inferences in applications.
  Illustrative examples are presented to demonstrate the wide applicability of
the IMU models. The proposed IMU framework, including many popular classical
urn models, not only offers a unify perspective for us to comprehend the urn
process, but also enables us to generate several novel urn models with
desirable properties.
