The Gaussian Transform
The Gaussian Transform
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高斯变换
DOI：
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发表时间：
2005
期刊：
影响因子：
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通讯作者：
T. Pun
中科院分区：
文献类型：
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作者：
T. Alecu;S. Voloshynovskiy;T. Pun
本文介绍了通用高斯变换，其目的是表示一个通用的对称分布作为一个无限混合高斯分布。我们从问题的数学公式开始，继续研究这种变换的存在条件。我们的分析导致推导的分析和数值工具的计算的高斯变换，主要是基于拉普拉斯和傅立叶变换，以及传入属性集（例如，变换的总和的独立变量）。最后，高斯变换以典型分布（例如高斯，拉普拉斯）的分析形式，以及广义高斯和广义柯西分布族的数值形式为例。
This paper introduces the general purpose Gaussian Transform, which aims at representing a generic symmetric distribution as an infinite mixture of Gaussian distributions. We start by the mathematical formulation of the problem and continue with the investigation of the conditions of existence of such a transform. Our analysis leads to the derivation of analytical and numerical tools for the computation of the Gaussian Transform, mainly based on the Laplace and Fourier transforms, as well as of the afferent properties set (e.g. the transform of sums of independent variables). Finally, the Gaussian Transform is exemplified in analytical form for typical distributions (e.g. Gaussian, Laplacian), and in numerical form for the Generalized Gaussian and Generalized Cauchy distributions families.