On comparing measures of sample skewness and kurtesis

Date of Publication

2001

Document Type

Bachelor's Thesis

Degree Name

Bachelor of Science in Mathematics

College

College of Science

Department/Unit

Mathematics and Statistics

Abstract/Summary

This research is an exposition of D. N. Joanes and C. A. Gill's study on Comparing Measures of Sample Skewness and Kurtosis. It focuses on the traditional measures of skewness and kurtosis, g1 and g2, respectively, and other measures of skewness and kurtosis adopted by statistical packages, such as SAS and SPSS G1 and G2, and MINITAB and BMP's b1 and b2.

Simulation studies were conducted to compare measures of sample skewness and kurtosis. MS Excel was used to generate data from uniform from 0 to 1, normal with mean 5 and variance 2, chi-square with 1, 15 and 30 degrees of freedom and t-distribution with 5 and 20 degrees of freedom. Property of least mean-squared error was used as criteria to determine best estimators for skewness and kurtosis.

It was found out that choice of best estimators of skewness and kurtosis are dependent on the sample size and whether the mean-squared error is dominated by a large variance or bias term. For uniform and normal distributions, b1 is the best estimator for skewness and b2 and g2, are good estimators kurtosis. For the chi-square with 1 degree of freedom, the measures G1 and G2 are best estimators of skewness and kurtosis, respectively. For greater degrees of freedom, b1 and g2 are best estimators of skewness and kurtosis respectively. For the t-distribution, the best estimator of skewness is b1. Moreover, b2 and g2 are good estimators of kurtosis for the t-distribution.

Abstract Format

html

Language

English

Format

Print

Accession Number

TU10762

Shelf Location

Archives, The Learning Commons, 12F, Henry Sy Sr. Hall

Physical Description

69 leaves

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