The Properties of a Decile-Based Statistic to Measure Symmetry and Asymmetry

Abstract

This paper studies a simple skewness measure to detect symmetry and asymmetry in samples. The statistic can be obviously applied with only three short central tendencies; i.e., the first and ninth deciles, and the median. The strength of the statistic to find symmetry and asymmetry is studied by employing numerous Monte Carlo simulations and is compared with some alternative measures by applying some simulation studies. The results show that the performance of this statistic is generally good in the simulation.

Keywords

• symmetry
• asymmetry
• measure of skewness
• decile
• monte carlo algorithm