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The purpose of this study is to extend the classical noncentral F-distribution under normal settings to noncentral closed skew F-distribution for dealing with independent samples from multivariate skew normal (SN) distributions.

Based on generalized Hotelling's T² statistics, confidence regions are constructed for the difference between location parameters in two independent multivariate SN distributions. Simulation studies show that the confidence regions based on the closed SN model outperform the classical multivariate normal model if the vectors of skewness parameters are not zero. A real data analysis is given for illustrating the effectiveness of our proposed methods.

This study’s approach is the first one in literature for the inferences in difference of location parameters under multivariate SN settings. Real data analysis shows the preference of this new approach than the classical method.

For the real data applications, the authors need to remove outliers first before applying this approach.

This study’s approach may apply many multivariate skewed data using SN fittings instead of classical normal fittings.

This paper is the research paper and the authors’ new approach has many applications for analyzing the multivariate skewed data.