A comparative Study of Four Estimators for Analyzing the Random Event Rate of the Poisson Process
Sohn, So Young
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In this paper, a random effect Poisson regression model is considered for prediction of the failure rate which would follow a lognormal distribution. A two stage procedure is used to obtain the regression estimator of the failure rate as well as the shrinkage estimator. These estimators are compared to both the raw estimator which entirely depends on the historical failure records and a shrinkage estimator in which a gamma distribution is used mistakenly in place of the lognormal prior distribution. Results of Monte-Carlo simulation indicate the following in terms of the MSE:(1)overall, the shrinkage estimator based on the lognormal prior distribution performs best;(2)with the failure rates (0-2.5),the performance of the shrinkage estimator based on the gamma distribution is not significantly different from that of the shrinkage estimator based on the lognormal distribution;(3)when there exists considerable variability in the failure rates(0-10),the raw estimator appears to replace shrinkage estimations. In terms of the Bias, the raw estimator performs better than the others.
The article of record as published may be found at https://doi.org/10.1080/00949659408811556
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