Performance of Some Estimators of Relative Variability - Ospina, Raydonal; Marmolejo-Ramos, Fernando (Frontiers in Applied Mathematics and Statistics, 2019)
The classic coefficient of variation (CV) is the ratio of the standard deviation to the mean and can be used to compare normally distributed data with respect to their variability, this measure has been widely used in many fields. In the Social Sciences, the CV is used to evaluate demographic heterogeneity and social aggregates such as race, sex, education and others. Data of this nature are usually not normally distributed, and the distributional characteristics can vary widely. In this sense, more accurate and robust estimator variations of the classic CV are needed to give a more realistic picture of the behaviour of collected data. In this work, we empirically evaluate five measures of relative variability, including the classic CV, of finite sample sizes via Monte Carlo simulations. Our purpose is to give an insight into the behaviour of these estimators, as their performance has not previously been systematically investigated. To represent different behaviours of the data, we considered some statistical distributions -- which are frequently used to model data across various research fields. To enable comparisons, we consider parameters of these distributions that lead to a similar range of values for the CV. Our results indicate that CV estimators based on robust statistics of scale and location are more accurate and give the highest measure of efficiency. Finally, we study the stability of a robust CV estimator in psychological and genetic data and compare the results with the traditional CV.