Date Approved

2009

Degree Type

Open Access Thesis

Degree Name

Master of Science (MS)

Department

Mathematics

Committee Member

C. J. Gardiner, PhD, Chair

Committee Member

Bette Warren, PhD

Committee Member

Kenneth Shiskowski, PhD

Abstract

Because the Poisson distribution is discrete, it is sometimes useful to use the continuous normal distribution as an approximation. In doing so, determining the accuracy of the approximation is important. Some issues of interest include: knowing how the error depends on the Poisson parameter, knowing when the approximation overestimates or underestimates the distribution, bounding the magnitude of the error, and determining if the approximation can be improved. This paper addresses these issues by examining how two types of absolute error measurements are affected by variations in the Poisson parameter; changes in the relative error are also examined. Generally, the error decays much like a power function of the parameter; therefore, curve fitting is used to bound the error. Finally, variations on the approximation are examined; these variations are often more accurate than the standard approximation.

Included in

Mathematics Commons

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