A collection of I similar items generates point event histories; for example, machines experience failures or operators make mistakes. Suppose the intervals between events are modeled as iid exponential (λ i), or the counts as Poisson (λ iti), for the ith item. Furthermore, so as to represent between-item variability, each individual rate parameter λ i, is presumed drawn from a fixed (super) population with density gλ(·;θ), θ being a vector parameter: a parametric empirical Bayes (PEB) setup. For gλ, specified alternatively as long-Student t(n) or gamma, we exhibit the results of numerical procedures for estimating superpopulation parameters θ and for describing pooled estimates of the individual rates λ i, obtained via Bayes's formula. Three data sets are analyzed, and convenient explicit approximate formulas are furnished for λ i estimates. In the Student-t case, the individual estimates are seen to have a robust quality.
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Technometrics
© 1987 American Statistical Association
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