Theses and Dissertations
Date of Award
Master of Science (MS)
Dr. George P. Yanev
Dr. Hansapani Rodrigo
Dr. Tamer F. Oraby
The motivation for this paper stems from the role Borel-Tanner (BT) distribution has as the distribution of the total outbreak number in epidemics modeled by branching processes. We briefly review Borel-Tanner distribution and its applications. In Chapter II we outline the Bayes decision problem, a construction for an Empirical Bayes (EB) estimator proposed by Liang  and discuss risk analysis. In Chapter III, the importance of randomization addressed and a classical construction of a monotonized EB estimator proposed by Houwalingen  is outlined. Lastly in Chapter IV we use R software to perform a Monte Carlo simulation and conduct a numerical study in which we construct data and estimators for the reproduction parameter of Borel-Tanner distribution. We implement a procedure outlined by Houwalingen to obtain a monotonized version of the EB estimator proposed by Liang . The estimators are assessed through risk analysis under squared error loss function and numerical study results are reviewed. The study suggests that the monotonized EB estimator outperforms the original EB estimator.
Soltero, Celestina Ruby, "Empirical Bayes Estimators and Borel-Tanner Distribution" (2019). Theses and Dissertations. 528.
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