An Alternative Goodness-of-fit Test for Normality with Unknown Parameters

Authors

Weiling ShiFollow

Document Type

Thesis

Degree

Master of Science (MS)

Major/Program

Statistics

First Advisor's Name

Zhenmin Chen

First Advisor's Committee Title

Committee Chair

Second Advisor's Name

Florence George

Second Advisor's Committee Title

Committee Member

Third Advisor's Name

Gauri Ghai

Third Advisor's Committee Title

Committee Member

Keywords

Goodness-of-fit test for normality, Monte Carlo Simulation, G test

Date of Defense

11-14-2014

Abstract

Goodness-of-fit tests have been studied by many researchers. Among them, an alternative statistical test for uniformity was proposed by Chen and Ye (2009). The test was used by Xiong (2010) to test normality for the case that both location parameter and scale parameter of the normal distribution are known. The purpose of the present thesis is to extend the result to the case that the parameters are unknown. A table for the critical values of the test statistic is obtained using Monte Carlo simulation. The performance of the proposed test is compared with the Shapiro-Wilk test and the Kolmogorov-Smirnov test. Monte-Carlo simulation results show that proposed test performs better than the Kolmogorov-Smirnov test in many cases. The Shapiro Wilk test is still the most powerful test although in some cases the test proposed in the present research performs better.

Identifier

FI14110735

Recommended Citation

Shi, Weiling, "An Alternative Goodness-of-fit Test for Normality with Unknown Parameters" (2014). FIU Electronic Theses and Dissertations. 1623.
https://digitalcommons.fiu.edu/etd/1623