A Bayesian Approach to Parameter and Reliability Estimation in the Poisson Distribution
- 1 February 1972
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Reliability
- Vol. R-21 (1) , 52-56
- https://doi.org/10.1109/tr.1972.5216172
Abstract
For life testing procedures, a Bayesian analysis is developed with respect to a random intensity parameter in the Poisson distribution. Bayes estimators are derived for the Poisson parameter and the reliability function based on uniform and gamma prior distributions of that parameter. A Monte Carlo procedure is implemented to make possible an empirical mean-squared error comparison between Bayes and existing minimum variance unbiased, as well as maximum likelihood, estimators. As expected, the Bayes estimators have mean-squared errors that are appreciably smaller than those of the other two.Keywords
This publication has 7 references indexed in Scilit:
- Bayesian Approach to Life Testing and Reliability EstimationJournal of the American Statistical Association, 1967
- The Efficiencies in Small Samples of the Maximum Likelihood and Best Unbiased Estimators of Reliability FunctionsJournal of the American Statistical Association, 1966
- Introduction to Probability and Statistics from a Bayesian ViewpointPublished by Cambridge University Press (CUP) ,1965
- Minimum Variance Unbiased Estimators for Poisson ProbabilitiesTechnometrics, 1962
- Sequential Life Tests in the Exponential CaseThe Annals of Mathematical Statistics, 1955
- Some Theorems Relevant to Life Testing from an Exponential DistributionThe Annals of Mathematical Statistics, 1954
- Life TestingJournal of the American Statistical Association, 1953