Goodness-of-fit Test for Uniformity on the Surface of a Unit Sphere Based on Generalized Inverse

摘要

We present a new test for uniform distribution on the surface of a unit sphere based on the Moore-Penrose inverse of the covariance matrix of the uniform distribution. The new test possesses symmetry which improves on the combination tests based on the center of mass and the moment of inertia. The asymptotic chi-squared distribution of the test statistic is obtained, the test has the nice properties as the combination tests and it is quite easy to implement.