标题： 一个偏态正态数据的Jarque-Bera检验 显示英文标题

标题： A Jarque-Bera test for skew normal data

摘要： 偏态正态分布定律在Azzalin（1985）中被引入，作为调整与正态分布有重要模式的不对称数据的一种替代方法。它已经被广泛研究。然而，为了捕捉其正态对应物研究的多样性和丰富性，还有许多工作要做。广义Jarque-Berra检验（GJBT）由Lo等人（2015），Da等人（2023）设计，适用于至少具有有限前八个矩的任意分布，作为Jarque-Bera（1987）检验的推广，该检验专门用于正态数据。在这里，我们将它具体化为偏态正态数据。当具体化为偏态正态分布时，该检验被证明在检测任何$\alpha\neq 0$的真实模型方面非常强大，并且无论数据规模如何，都会拒绝正态分布（$\alpha=0$）。我们引入了样本复制方法，以达到检验的高效水平。 显示英文摘要

摘要： 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.