The Properties of a Decile-Based Statistic to Measure Symmetry and Asymmetry
Mohammad Reza Mahmoudi,
Roya Nasirzadeh,
Dumitru Baleanu,
Kim-Hung Pho
Affiliations
Mohammad Reza Mahmoudi
Institute of Research and Development, Duy Tan University, Da Nang 550000, Vietnam
Roya Nasirzadeh
Department of Statistics, Faculty of Science, Fasa University, Fasa, Fars 7461686131, Iran
Dumitru Baleanu
Department of Mathematics, Faculty of Art and Sciences, Cankaya University, Ankara 06530, Turkey
Kim-Hung Pho
Fractional Calculus, Optimization and Algebra Research Group, Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City 72915, Vietnam
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.
