Immigrated urn models - asymptotic properties and applications

TL;DR

This paper introduces a new class of immigrated urn (IMU) models that incorporate an immigration mechanism, offering more efficient and powerful statistical tools for applications like clinical trials.

Contribution

The paper proposes a general IMU framework that unifies classical urn models and introduces novel models with improved variability and inference properties.

Findings

IMU models have smaller variabilities than classical urn models.

IMU models provide more powerful statistical inferences.

The framework unifies and extends existing urn models.

Abstract

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.