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Tail probabilities of the limiting null distributions of the Anderson-Stephens statistics


  • Satoshi Kuriki

    (The Institute of Statistical Mathematics)

  • Akimichi Takemura

    (Faculty of Economics, University of Tokyo)


For the purpose of testing the spherical uniformity based on i.i.d. directional data (unit vectors) zi, i =1,...,n, Anderson and Stephens (1972) proposed testing procedures based on the statistics Smax = maxuS (u) and S min = minuS (u), where u is a unit vector and nS (u) is the sum of square of u'zi's. In this paper we also consider another test statistic Srange = Smax -Smin. We provide formulas for the P-values of Smax , Smin , Srange by approximating tail probabilities of the limiting null distributions by means of the tube method, an integral-geometric approach for evaluating tail probability of the maximum of a Gaussian random field. Monte Carlo simulations for examining the accuracy of the approximation and for the power comparison of the statistics are given.

Suggested Citation

  • Satoshi Kuriki & Akimichi Takemura, 2000. "Tail probabilities of the limiting null distributions of the Anderson-Stephens statistics," CIRJE F-Series CIRJE-F-77, CIRJE, Faculty of Economics, University of Tokyo.
  • Handle: RePEc:tky:fseres:2000cf77

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