On Some Test Statistics for Testing the Population Skewness and Kurtosis: An Empirical Study

Authors

Yawen GuoFollow

Document Type

Thesis

Degree

Master of Science (MS)

Major/Program

Statistics

First Advisor's Name

B.M. Golam Kibria

First Advisor's Committee Title

Committee Chair

Second Advisor's Name

Wensong Wu

Second Advisor's Committee Title

Committee Member

Third Advisor's Name

Florence George

Third Advisor's Committee Title

Committee Member

Keywords

Test Statistics, Skewness, Kurtosis, Bootstrap, Simulation

Date of Defense

8-26-2016

Abstract

The purpose of this thesis is to propose some test statistics for testing the skewness and kurtosis parameters of a distribution, not limited to a normal distribution. Since a theoretical comparison is not possible, a simulation study has been conducted to compare the performance of the test statistics. We have compared both parametric methods (classical method with normality assumption) and non-parametric methods (bootstrap in Bias Corrected Standard Method, Efron’s Percentile Method, Hall’s Percentile Method and Bias Corrected Percentile Method). Our simulation results for testing the skewness parameter indicate that the power of the tests differs significantly across sample sizes, the choice of alternative hypotheses and methods we chose. For testing the kurtosis parameter, the simulation results suggested that the classical method performs well when the data are from both normal and beta distributions and bootstrap methods are useful for uniform distribution especially when the sample size is large.

Identifier

FIDC001189

Recommended Citation

Guo, Yawen, "On Some Test Statistics for Testing the Population Skewness and Kurtosis: An Empirical Study" (2016). FIU Electronic Theses and Dissertations. 3045.
https://digitalcommons.fiu.edu/etd/3045