Many statistics are based on functions of sample moments. Important examples are the sample variance s2(n), the sample coefficient of variation SV (n), the sample dispersion SD(n) and the non-central t-statistic t(n). The definition of these quantities makes clear that the vector defined by (?ni=1Xi, ?ni=1Xi2)plays an important role. In the paper we obtain conditions under which the vector (X,X2) belongs to a bivariate domain of attraction of a stable law. Applying simple transformations then leads to a full discussion of the asymptotic behaviour of SV(n) and t(n).
Evaluating the Goodness of the Sample Coefficient of Variation via Discrete Uniform
Distribution
