On comparing measures of sample skewness and kurtesis

• Main Authors: Pacleb, Michelle I., Mabutas, Pearl Aileen B.
• Format: text
• Language: English
• Published: Animo Repository 2001
• Online Access: https://animorepository.dlsu.edu.ph/etd_bachelors/17185
• Institution: De La Salle University

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.