Developing an A Priori Approach to Sample Size Determination for Estimating the Inverse Coefficient of Variation in Skew-Normal Populations

Abstract The inverse coefficient of variation (ICV) has gained significant attention as a preferred measure in fields such as economics, healthcare, and clinical trials. This makes it desirable for researchers to determine appropriate sample sizes when using sample-based estimators to estimate the population ICV. In this paper, we derive both the moment and Bayes estimators of the ICV under a skew-normal distribution, and use them to develop equations for sample size determination based on the A Priori Procedure (APP). The multivariate skew-normal model introduces a flexible dependence structure through its shape parameters, allowing correlation patterns that cannot be captured by the standard multivariate normal model. This dependence directly affects the behavior of the ICV estimators and plays an important role in determining the required sample sizes, highlighting the benefits of jointly modeling skewness and dependence. We further construct confidence intervals and evaluate their coverage probabilities via Monte Carlo simulations. Finally, a real-world dataset is analyzed to illustrate the practical applicability of the proposed methodology.