Asymptotic results for a generalized Pòlya urn with delay and an applications to clinical trials

Abstract

In this paper a new Pòlya urn model is introduced and studied; in particular, a strong law of large numbers and two central limit theorems are proven. This urn generalizes a model studied in Berti et al. (2004), May et al. (2005) and in Crimaldi (2007) and it has natural applications in clinical trials. Indeed, the model include both delayed and missing (or null) responses. Moreover, a connection with the conditional identity in distribution of Berti et al. (2004) is given.