Several methods for generating random variables with univariate and multivariate Wallenius' and Fisher's noncentral hypergeometric distributions are developed. Methods for the univariate distributions include: simulation of urn experiments, inversion by binary search, inversion by chop-down search from the mode, ratio-of-uniforms rejection method, and rejection by sampling in the t domain. Meth...

Wassily Hoeffding, in his 1963 paper, introduces a procedure to derive inequalities between distributions. This method relies on finding a martingale coupling between the two random variables. I have developed a construction that establishes such couplings in various urn models. I use this construction to prove the inequality between the hypergeometric and binomial random variables that appears...

In this paper, we present several probabilistic transforms related to classical urn models. These transforms render the dependent random variables describing the urn occupancies into independent random variables with appropriate distributions. This simplifies the analysis of a large number of problems for which a function under investigation depends on the urn occupancies. The approach used for...

Words of fixed size q are commonly referred to as q-grams. We consider the problem of q-gram filtration, a method commonly used to speed up sequence comparison. We are interested in the statistics of the number of q-grams common to two random texts (where multiplicities are not counted) in the non uniform Bernoulli model. In the exact and dependent model, when omitting border effects, a q-gram ...

We propose a Bayesian nonparametric model to estimate rating migration matrices and default probabilities using the reinforced urn processes (RUP) introduced in Muliere et al. (2000). The estimated default probability becomes our prior information in a parametric model for the prediction of the number of bankruptcies, with the only assumption of exchangeability within rating classes. The Polya ...

The User Requirements Notation (URN) combines goals and scenarios in order to help capture and reason about user requirements prior to detailed design. In terms of application areas, this emerging standard targets reactive systems in general, with a particular emphasis on telecommunications systems and services. However, URN can also be applied to business process modeling. In this paper, we il...

Generalized Polya urn models can describe the dynamics of finite populations of interacting genotypes. Three basic questions these models can address are: Under what conditions does a population exhibit growth? On the event of growth, at what rate does the population increase? What is the long term behavior of the distribution of genotypes? To address these questions, we associate a mean limit ...

We derive the distribution of the number of infections among unvaccinated and vaccinated individuals for model 1 (leaky) and model 2 (all/nothing) vaccines, assuming random mixing of a homogeneous population. For all/nothing vaccines, we show that the distribution of the number of infected vaccinated individuals conditioning on n observed infections follows a hypergeometric distribution, and th...

The prevalence of categorical observations that are unique in a sample and also still unique in the population are usually taken as the measure of the overall risk of disclosure in the sample data. Samuels (1998) suggested adopting evolutionary processes and their associated urn models as a framework for estimating this prevalence. We re-examine his proposal and suggest several extensions that ...