Theoretical Statistics and Mathematics Unit, ISI Delhi

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

by Yogendra P. Chaubey, Murari Singh and Debaraj Sen

Coefficient of variation (CV) plays an important role in statistical practice and since an IG distribution may provide a good model for positive and positively skewed data, its distributional properties are of interest to practitioners. The variance stabilizing and symmetrizing transformations are often used for approximating the distribution in practice. In this paper we study the symmetrizing transformation of the square of the sample CV along the lines of Chaubey and Mudholkar (1983) that requires numerical techniques. The variance stabilizing transformation, on the other hand, is explicitly available, however its performance as an approximation to the distribution is extremely poor. An analysis of the symmetrizing transformation guided the authors to investigate the power transformation family which yielded an excellent approximation to the distribution function of the sample CV for sample sizes as small as $10$ in the practical range of population CV. The resulting approximation is compared with others and its usefulness is illustrated in hypothesis testing example.

isid/ms/2015/02 [fulltext]

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