On Blest’s Measure of Kurtosis Adjusted for Skewness

Abstract

We reconsider the derivation of Blest’s (2003) skewness adjusted version of the classical moment-based coefficient of kurtosis and propose an adaptation of it which generally eliminates the effects of asymmetry a little more successfully. Lower bounds are provided for the two skewness adjusted kurtosis moment measures as functions of the classical coefficient of skewness. The results from a Monte Carlo experiment designed to investigate the sampling properties of numerous moment-based estimators of the two skewness adjusted kurtosis measures are used to identify those estimators with lowest mean squared error for small to medium sized samples drawn from distributions with varying levels of asymmetry and tailweight.

Keywords:

• Asymmetry
• Estimation
• Lower bounds
• Moment-based measures
• Sinh-arcsinh transformation.

Mathematics Subject Classification:

• 62A01; 62G05.