SOME Q-Q PROBABILITY PLOTS TO TEST SPHERICAL AND ELLIPTIC SYMMETRY

This article proposes some probability plots are proposed to test sphe rical and elliptical symmetry in terms of some invariant statistics un der orthogonal transformations. Some correlation coefficients as numer ical measures of detecting deviation from spherical or elliptical symm etry are recommended, and the empirical percentiles of these correlati on coefficients are calculated by simulation. The simulation results f or data sets from 12 different populations show that the new plots are useful for testing spherical and elliptical symmetry. Some discussion is given also.