Inference for coefficient of variation and noncentrality parameters

The coefficient of variation establishes the degree of variability of a dataset in relation to the mean. Taking advantage of its dimensionless characteristic, the coefficient of variation is used to quantify the variability of data in several research fields. Going beyond point estimation, it is often important to know information about the value of the population coefficient of variation, through confidence intervals or hypothesis tests. Limit distributions arising from an increase in sample noncentrality and not from sample size have been obtained in Mexia and Oliveira (2010) and Nunes et al. (2013), which may be useful to perform inference. In this paper we consider inference for coefficient of variation and noncentrality parameters, obtaining, for the normal case, confidence intervals and testing hypothesis through duality. The results for coefficient of variation are applied to normal samples, linear regression and products of variables, while the results on the noncentrality parameters were applied to one-way and multi-way ANOVA.