Several families of statistical distributions have been used to model financial data. The four-parameter generalized beta of the second kind (GB2) and five-parameter skewed generalized t (SGT) have been fit to return and log-return data, respectively. We introduce the skewed generalized log-t (SGLT) distribution and note that the GB2 and SGLT share such distributions as the asymmetric log-Laplace (ALL), log-Laplace (LL), and log-normal (LN). We then compare the relative performance of the GB2 and SGLT in modeling the distribution of daily, weekly, and monthly stock return data. We find that the GB2 and SGLT perform similarly and that the three-parameter log-t (LT) distribution is quite robust.

中文翻译：

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GB2 和偏态广义 log-t 分布与金融应用的比较

几个统计分布族已被用来对财务数据建模。第二类四参数广义 beta (GB2) 和五参数偏斜广义 t (SGT) 已分别拟合返回数据和对数返回数据。我们引入偏斜广义 log-t (SGLT) 分布，并注意到 GB2 和 SGLT 共享非对称 log-Laplace (ALL)、log-Laplace (LL) 和 log-normal (LN) 等分布。然后，我们比较 GB2 和 SGLT 在对每日、每周和每月股票收益数据的分布进行建模时的相对性能。我们发现 GB2 和 SGLT 的表现相似，并且三参数 log-t (LT) 分布非常稳健。