Document Type

Thesis

Degree

Master of Science (MS)

Department

Mathematical Sciences

First Advisor's Name

Hassan Zahedi

First Advisor's Committee Title

Major Professor

Second Advisor's Name

Florence George

Third Advisor's Name

Zhenmin Chen

Keywords

Testing Normality, Hoeffding's D Statistic

Date of Defense

3-21-2014

Abstract

The purposes of the thesis were to review some of the existing methods for testing normality and to investigate the use of generated data combined with observed to test for normality. The approach to testing for normality is in contrast to the existing methods which are derived from observed data only. The test of normality proposed follows a characterization theorem by Bernstein (1941) and uses a test statistic D*, which is the average of the Hoeffding’s D-Statistic between linear combinations of the observed and generated data to test for normality.

Overall, the proposed method showed considerable potential and achieved adequate power for many of the alternative distributions investigated. The simulation results revealed that the power of the test was comparable to some of the most commonly used methods of testing for normality. The test is performed with the use of a computer-based statistical package and in general takes a longer time to run than some of the existing methods of testing for normality.

Identifier

FI14040851

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