Theses and Dissertations

Date of Award

8-2019

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematics

First Advisor

Dr. George P. Yanev

Second Advisor

Dr. Hansapani Rodrigo

Third Advisor

Dr. Tamer F. Oraby

Abstract

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 [9] and discuss risk analysis. In Chapter III, the importance of randomization addressed and a classical construction of a monotonized EB estimator proposed by Houwalingen [14] 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.

Comments

Copyright 2019 Celestina Ruby Soltero. All Rights Reserved.

https://go.openathens.net/redirector/utrgv.edu?url=https://www.proquest.com/dissertations-theses/empirical-bayes-estimators-borel-tanner/docview/2312584825/se-2?accountid=7119

Download

Included in

Mathematics Commons

Share

COinS