An occupancy distribution arising in a limiting dilution assay for HIV-1

We describe a multivariate discrete distribution arising in a Bayesian analysis and design of a serial dilution assay for HIV-1 cells as a part of a syringe exchange among injection drug users. A solution containing N living viral cells is diluted in several stages. The laboratory procedures indicate which stages contain at least one live viral cell when the dilute aliquot are fermented. We assume a gamma prior distribution on N and describe the joint multivariate marginal distribution of the outcomes of the aliquot. We provide expressions for the joint moments and graphically illustrate the univariate distribution.