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摘要翻译：
出于对金融数学中丰富且易于处理的分布的参数族的需求，无论是在定价和风险管理环境中，还是考虑到更广泛的统计应用，我们研究了一种将偏度或峰度引入对称或其他分布的新技术。我们使用一个“嬗变”映射，它是一个分布的累积分布函数与另一个分布的逆累积分布（分位数）函数的函数组合。与Gram-Charlier方法不同的是，这种方法无需借助渐近展开，因此避免了经常与之相关的病理。我们可以用这种方法生成的参数分布的例子包括斜均匀分布、斜指数分布、斜正态分布和斜峭正态分布。
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英文标题：
《The alchemy of probability distributions: beyond Gram-Charlier
expansions, and a skew-kurtotic-normal distribution from a rank transmutation
map》
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作者：
William T. Shaw, Ian R.C. Buckley
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最新提交年份：
2009
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分类信息：
一级分类：Quantitative Finance 数量金融学
二级分类：Statistical Finance 统计金融
分类描述：Statistical, econometric and econophysics analyses with applications to financial markets and economic data
统计、计量经济学和经济物理学分析及其在金融市场和经济数据中的应用
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一级分类：Quantitative Finance 数量金融学
二级分类：Computational Finance 计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
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英文摘要：
Motivated by the need for parametric families of rich and yet tractable distributions in financial mathematics, both in pricing and risk management settings, but also considering wider statistical applications, we investigate a novel technique for introducing skewness or kurtosis into a symmetric or other distribution. We use a "transmutation" map, which is the functional composition of the cumulative distribution function of one distribution with the inverse cumulative distribution (quantile) function of another. In contrast to the Gram-Charlier approach, this is done without resorting to an asymptotic expansion, and so avoids the pathologies that are often associated with it. Examples of parametric distributions that we can generate in this way include the skew-uniform, skew-exponential, skew-normal, and skew-kurtotic-normal.
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PDF链接：
https://arxiv.org/pdf/0901.0434
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