Inference for the normal coefficient of variation: an approximate marginal likelihood approach

A. Wong () and X. Shi ()
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A. Wong: York University
X. Shi: University of British Columbia

Statistical Papers, 2025, vol. 66, issue 1, No 12, 17 pages

Abstract: Abstract In applied statistics, the coefficient of variation (CV) is commonly reported as a measure of relative variability of the data. However, confidence intervals for CV are rarely reported because the existing methodologies are either simple to understand but do not give accurate results or vice versa. In this paper, we assumed data are from a normal population, and an approximate marginal likelihood function for the normal CV is derived from the Studentization method, and a Bartlett-type correction method is proposed to obtain accurate inferential for the normal CV. Moreover, if the populations are measured using different scales, comparing CVs among the populations is a more appropriate way to determine if the variability among the populations is heterogeneous. The proposed Bartlett-type correction method is extended to test if the normal CVs are homogeneous for two or more normal populations. Numerical examples are given to illustrate the accuracy of the proposed method.

Keywords: Bartlett correction; Confidence distribution function; Homogeneity of coefficient of variation; Laplace approximation; Log-likelihood ratio statistic; Studentization. (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s00362-024-01622-5

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