Abstract
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 i t i ,) 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 g λ (·; θ), θ being a vector parameter: a parametric empirical Bayes (PEB) setup. For g λ, specified alternatively as log-Student t(n) or gamma, we exhibit the results of numerical procedures for estimating superpopulation parameters ll 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.
Keywords
MathematicsBayes' theoremStatisticsEvent (particle physics)Parametric statisticsPoisson distributionPoint estimationPopulationEconometricsExponential familyApplied mathematicsBayesian probability
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Publication Info
- Year
- 1987
- Type
- article
- Volume
- 29
- Issue
- 1
- Pages
- 1-15
- Citations
- 75
- Access
- Closed
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Cite This
Donald P. Gaver,
I. G. O’Muircheartaigh
(1987).
Robust Empirical Bayes Analyses of Event Rates.
Technometrics
, 29
(1)
, 1-15.
https://doi.org/10.1080/00401706.1987.10488178
Identifiers
- DOI
- 10.1080/00401706.1987.10488178