We develop a likelihood-ratio test for discriminating between the g-and-h and the g distribution, which is a special case of the former obtained when the parameter h is equal to zero. The g distribution is a shifted lognormal, and is therefore suitable for modeling economic and financial quantities. The g-and-h is a more flexible distribution, capable of fitting highly skewed and/or leptokurtic data, but is computationally much more demanding. Accordingly, in practical applications the test is a valuable tool for resolving the tractability-flexibility trade-off between the two distributions. Since the classical result for the asymptotic distribution of the test is not valid in this setup, we derive the null distribution via simulation. Further Monte Carlo experiments allow us to estimate the power function and to perform a comparison with a similar test proposed by Xu and Genton (Comput Stat Data Anal 91:78–91, 2015). Finally, the practical relevance of the test is illustrated by two risk management applications dealing with operational and actuarial losses.

我们开发了一种似然比检验来区分 g-and-h 和 g 分布，这是前者的特例，当参数h等于零。g 分布是平移对数正态分布，因此适用于对经济和金融数量进行建模。g-and-h 是一种更灵活的分布，能够拟合高度偏斜和/或高峰态数据，但在计算上要求更高。因此，在实际应用中，该测试是解决两个分布之间的易处理性-灵活性权衡的宝贵工具。由于测试渐近分布的经典结果在此设置中无效，我们通过模拟得出零分布。进一步的蒙特卡罗实验使我们能够估计幂函数并与 Xu 和 Genton 提出的类似测试进行比较（Comput Stat Data Anal 91:78–91, 2015）。最后，