Asymptotic Normality and the Coefficient of Variation

Abstract

Abstract It is common to assume that if skewness tends, under specified circumstance, to zero, the allied distribution tends to normality. In some recent published research work, it was empirically demonstrated (via real data and a sample of theoretical distributions) that skewness and the coefficient of variation are statistically positively linearly related. This result is not intuitive and not yet mathematically proved. We explore here the scope and prevalence of this phenomenon, relating to both known theoretical results and to published data‐based examples for applying a normalizing exponential transformation. Conclusions are derived.