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New nonparametric tests for testing homogeneity of scale parameters against umbrella alternative


  • Gaur, Anil
  • Mahajan, Kalpana K.
  • Arora, Sangeeta


Three nonparametric tests for several sample scale problem against umbrella alternative, when the peak of the umbrella is known, are proposed. The proposed statistics have the advantage of not requiring the several distribution functions to have a common median, but rather any common quantile of order α,0≤α≤1, (not necessarily 1/2) which is assumed to be known. The proposed tests are compared with each other in the Pitman asymptotic relative efficiency sense for different distributions.

Suggested Citation

  • Gaur, Anil & Mahajan, Kalpana K. & Arora, Sangeeta, 2012. "New nonparametric tests for testing homogeneity of scale parameters against umbrella alternative," Statistics & Probability Letters, Elsevier, vol. 82(9), pages 1681-1689.
  • Handle: RePEc:eee:stapro:v:82:y:2012:i:9:p:1681-1689
    DOI: 10.1016/j.spl.2012.05.009

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    References listed on IDEAS

    1. A. Shanubhogue, 1988. "Distrubition-free test for homogeneity against stochastic ordering," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 35(1), pages 109-119, December.
    2. Singh, Parminder & Liu, Wei, 2006. "A test against an umbrella ordered alternative," Computational Statistics & Data Analysis, Elsevier, vol. 51(3), pages 1957-1964, December.
    3. Mahajan, Kalpana K. & Gaur, Anil & Arora, Sangeeta, 2011. "A nonparametric test for a two-sample scale problem based on subsample medians," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 983-988, August.
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    Cited by:

    1. Kiatsupaibul, Seksan & J. Hayter, Anthony & Liu, Wei, 2017. "Rank constrained distribution and moment computations," Computational Statistics & Data Analysis, Elsevier, vol. 105(C), pages 229-242.


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