A class of uniform tests for goodness-of-fit of the multivariate \(L_p\)-norm spherical distributions and the \(l_p\)-norm symmetric distributions

  • Jiajuan LiangEmail author
  • Kai Wang Ng
  • Guoliang Tian


In this paper we employ the conditional probability integral transformation (CPIT) method to transform a d-dimensional sample from two classes of generalized multivariate distributions into a uniform sample in the unit interval \((0,\,1)\) or in the unit hypercube \([0,\,1]^{d-1}\) (\(d\ge 2\)). A class of existing uniform statistics are adopted to test the uniformity of the transformed sample. Monte Carlo studies are carried out to demonstrate the performance of the tests in controlling type I error rates and power against a selected group of alternative distributions. It is concluded that the proposed tests have satisfactory empirical performance and the CPIT method in this paper can serve as a general way to construct goodness-of-fit tests for many generalized multivariate distributions.


Goodness-of-fit Monte Carlo study \(L_p\)-norm spherical distribution \(l_p\)-norm symmetric distribution Uniformity 


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© The Institute of Statistical Mathematics, Tokyo 2017

Authors and Affiliations

  1. 1.College of BusinessUniversity of New HavenWest HavenUSA
  2. 2.Department of Statistics and Actuarial ScienceThe University of Hong KongHong KongChina
  3. 3.Department of MathematicsSouthern University of Science and TechnologyNanshan DistrictChina

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