In this paper, we develop a multistage approach for estimating the mean of a bounded variable. We first focus on the multistage estimation of a binomial parameter and then generalize the estimation methods to the case of general bounded random variables. A fundamental connection between a binomial parameter and the mean of a bounded variable is established. Our multistage estimation methods rig...

In this paper, we develop a multistage approach for estimating the mean of a bounded variable. We first focus on the multistage estimation of a binomial parameter and then generalize the estimation methods to the case of general bounded random variables. A fundamental connection between a binomial parameter and the mean of a bounded variable is established. Our multistage estimation methods rig...

BACKGROUND Analyses of multicenter studies often need to account for center clustering to ensure valid inference. For binary outcomes, it is particularly challenging to properly adjust for center when the number of centers or total sample size is small, or when there are few events per center. Our objective was to evaluate the performance of generalized estimating equation (GEE) log-binomial an...

Various statistical methods have been used to measure the impact of treatment on chronic obstructive pulmonary disease (COPD) exacerbations. Poisson regression has recently been recommended as the appropriate method but the model does not satisfactorily account for variability between patients. In contrast, use of a negative binomial model, which corresponds to assuming a separate Poisson param...

We introduce new kinds of states of quantized radiation fields, which are the superpositions of negative binomial states. They exhibit remarkable non-classical properties and reduce to Schrödinger cat states in a certain limit. The algebras involved in the even and odd negative binomial states turn out to be generally deformed oscillator algebras. It is found that the even and odd negative bino...

This paper explores the potential of transformation and other schemes in constructing a sequence of simple binomial processes that weakly converges to the desired diffusion limit. Convergence results are established for valuing both European and American contingent claims when the underlying asset prices are approximated by simple binomial processes. We also demonstrate how to construct reflect...