This article presents a new empirical Bayes estimator (EBE) and a shrinkage estimator for determining the relative potency from several multivariate bioassays by incorporating prior information on the model parameters based on Jeffreys' rules. The EBE can account for any extra variability among the bioassays, and if this extra variability is 0, then the EBE reduces to the maximum likelihood estimator for combinations of multivariate bioassays. The shrinkage estimator turns out to be a compromise of the prior information and the estimator from each multivariate bioassay, with the weights depending on the prior variance.

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If g ( x )is the number of journals having x references, we speak of a size-frequency relationship. If f ( r ) is the number of references in a journal of rank r, we speak of a rankfrequency relationship. In the former we can estimate the number of journals, given the number of references; in the latter we can estimate the number of references given the rank of the journal. In this paper we prove a statistical relationship which links these two types of productivity distributions.