A Jarque-Bera test for skew normal data

TL;DR

This paper adapts the General Jarque-Berra Test specifically for skew normal data, demonstrating its high power in distinguishing skew normal from normal distributions and introducing sample duplication for improved efficiency.

Contribution

It specializes the GJBT to skew normal distributions and shows its effectiveness, along with a novel use of sample duplication to enhance test efficiency.

Findings

Test is highly powerful for skew normal data with non-zero skewness

Test reliably rejects normal law when skewness is present

Sample duplication improves test efficiency

Abstract

The skew normal law has been introduced in Azzalin (1985) as an alternative to adjusting asymmetric data that share important patterns with the normal law. It has been extensively studied. However, there is so much to do in order to catch the diversity and the richness of the investigation of its normal counterpart. The General Jarque-Berra Test (GJBT) has been devised by Lo et al. (2015), Da et al. (2023) for arbitrary laws with at least finite first eight moments, as a generalization of the Jarque-Bera (1987) test that was specially set up for normal data. Here, we particularize it to skew normal data. When particularized in the skew normal law, this test is proven to be extremely powerful in detecting the true model for any $\alpha\neq 0$ and rejected the normal law ($\alpha=0$) whatever be the size of the data. We introduced the use of the samples duplication method to reach a high level of efficiency for the test.