A comparative Study of Four Estimators for Analyzing the Random Event Rate of the Poisson Process
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Authors
Sohn, So Young
Subjects
Shrinkage estimator
Maximum likelihood estimation
Lognormal distribution
Two-Stage Estimation
Poisson regression
Maximum likelihood estimation
Lognormal distribution
Two-Stage Estimation
Poisson regression
Advisors
Date of Issue
1994
Date
1994
Publisher
Taylor & Francis
Language
Abstract
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.
Type
Article
Description
The article of record as published may be found at https://doi.org/10.1080/00949659408811556
Series/Report No
Department
Operations Research (OR)
Organization
Naval Postgraduate School (U.S.)
Identifiers
NPS Report Number
Sponsors
Naval Postgraduate School
Funding
Format
10 p.
Citation
Sohn, So Young. "A comparative study of four estimators for analyzing the random event rate of the Poisson process." Journal of Statistical Computation and Simulation 49.1-2 (1994): 1-10.
Distribution Statement
Rights
This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.