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Distributions Generated by Transformation of Scale Using an Extended Cauchy-Schlomilch Transformation

机译：使用扩展的柯西-施洛米奇变换通过尺度变换生成的分布

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摘要

Baker (2008) shows how more flexible densities on IR~+ can be generated from others by applying the Cauchy-Schlomilch transformation to the abscissa. Such "transformation of scale" is not even guaranteed to provide integrable functions in general. The appeal of the Cauchy-Schlomilch transformation is that it automatically does so; moreover, the normalising constant is unaffected and hence immediately available. In this paper, we fit the original Cauchy-Schlomilch transformation into a broader framework of novel extended Cauchy-Schlomilch transformations based on self-inverse functions, and propose the corresponding newly generated densities which also retain the same normalising constant. As well as providing parallels with, and extensions of, the many properties of the new densities developed by Baker, we investigate the skewness properties of both original and extended Cauchy-Schlomilch-based distributions via application of a recently proposed density-based approach to quantifying asymmetry.
机译：Baker（2008）展示了如何通过将Cauchy-Schlomilch变换应用于横坐标来从其他坐标中生成更灵活的IR〜+密度。通常，这种“规模转换”甚至不能保证提供可集成的功能。 Cauchy-Schlomilch转换的吸引力在于它会自动这样做。此外，归一化常数不受影响，因此立即可用。在本文中，我们将原始的Cauchy-Schlomilch变换拟合到基于自反函数的新颖的扩展Cauchy-Schlomilch变换的更广阔的框架中，并提出相应的新生成的密度，这些密度也保持相同的归一化常数。除了提供与贝克开发的新密度的许多特性的相似之处和扩展之外，我们还通过应用最近提出的基于密度的方法对原始和扩展的柯西-斯洛米尔奇分布的偏度特性进行了研究不对称。

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