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Symmetrizing and Variance Stabilizing Transformations of Sample Coefficient of Variation from Inverse Gaussian Distribution

Author

Listed:
  • Yogendra P. Chaubey

    (Department of Mathematics and Statistics, Concordia University)

  • Murari Singh

    (International Center for Agricultural Research in the Dry Areas)

  • Debaraj Sen

    (Department of Mathematics and Statistics, Concordia University)

Abstract

Coefficient of variation (CV) plays an important role in statistical practice; however, its sampling distribution may not be easy to compute. In this paper, the distributional properties of the sample CV from an inverse Gaussian distribution are investigated through transformations. Specifically, the symmetrizing transformation as outlined in Chaubey and Mudholkar (1983), that requires numerical techniques, is contrasted with the explicitly available variance stabilizing transformation (VST). The symmetrizing transformation scores very high as compared to the VST, especially in a power family. The usefulness of the resulting approximation is illustrated through a numerical example.

Suggested Citation

  • Yogendra P. Chaubey & Murari Singh & Debaraj Sen, 2017. "Symmetrizing and Variance Stabilizing Transformations of Sample Coefficient of Variation from Inverse Gaussian Distribution," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 79(2), pages 217-246, November.
    • Handle: RePEc:spr:sankhb:v:79:y:2017:i:2:d:10.1007_s13571-017-0136-z
    DOI: 10.1007/s13571-017-0136-z
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    References listed on IDEAS

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    1. David Hinkley, 1977. "On Quick Choice of Power Transformation," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 26(1), pages 67-69, March.
    2. Norbert Henze & Bernhard Klar, 2002. "Goodness-of-Fit Tests for the Inverse Gaussian Distribution Based on the Empirical Laplace Transform," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 54(2), pages 425-444, June.
    3. Govind Mudholkar & Rajeshwari Natarajan, 2002. "The Inverse Gaussian Models: Analogues of Symmetry, Skewness and Kurtosis," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 54(1), pages 138-154, March.
    4. Chaubey, Yogendra P. & Sen, Debaraj & Saha, Krishna K., 2014. "On testing the coefficient of variation in an inverse Gaussian population," Statistics & Probability Letters, Elsevier, vol. 90(C), pages 121-128.
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