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

Author(s): Yogendra P. Chaubey, Debaraj Sen and Murari Singh
Issue: Volume 79 Series B Part 2 Year 2017
Pages: 217 -- 246
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.
AMS (2000) subject classification. Primary 62E17; Secondary 62E30, 62E15, 62F03, 62E20, 62E25.
Keywords and phrases: Coefficient of variation, Inverse Gaussian distribution, Symmetrizing transformation, Variance stabilizing transformation