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Some Q-Q Probability Plots to Test Spherical and Elliptical Symmetry |
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| Authors: | Run-Ze Li Kai-Tai Fang Li-Xing Zhu |
| Institution: | 1. Department of Statistics , University of North Carolina , Chapel Hill , NC , 27599-3260 , USA;2. Department of Mathematics , Hong Kong Baptist University, Hong Kong and Institute of Applied Mathematics, Chinese Academy of Sciences , Beijing , 100080 , China;3. Probability Lab, Institute of Applied Mathematics, Chinese Academy of Sciences , Beijing , 100080 , China |
| Abstract: | Abstract This article proposes some probability plots are proposed to test spherical and elliptical symmetry in terms of some invariant statistics under orthogonal transformations. Some correlation coefficients as numerical measures of detecting deviation from spherical or elliptical symmetry are recommended, and the empirical percentiles of these correlation coefficients are calculated by simulation. The simulation results for data sets from 12 different populations show that the new plots are useful for testing spherical and elliptical symmetry. Some discussion is given also. |
| Keywords: | Beta distribution Elliptical distribution F-distribution Invariant statistics Probability plot Q-Q plot Robust statistics Spherical distribution t-distribution |