标题： 一个易于处理的概率分布及其在三维统计中的应用 显示英文标题

标题： A Tractable Probability Distribution with Applications in Three-Dimensional Statistics

摘要： 本文介绍并刻画了一类适用于三维随机空间中范数分布的新连续概率分布族，特别是适用于具有非零均值的三个随机高斯变量的欧几里得范数的分布。该分布定义在半无限范围$[0,\infty)$上，并以其计算上的可处理性而著称。在此基础上，我们还引入了另一族连续概率分布，适用于三维随机空间中的功率分布。尽管这些分布之前未知，但它们对许多应用具有吸引力，本文讨论了其中的一些应用。 显示英文摘要

摘要： This paper introduces and characterizes a new family of continuous probability distributions applicable to norm distributions in three-dimensional random spaces, specifically for the Euclidean norm of three random Gaussian variables with non-zero means. The distribution is specified over the semi-infinite range $[0,\infty)$ and is notable for its computational tractability. Building on this foundation, we also introduce a separate family of continuous probability distributions suitable for power distributions in three-dimensional random spaces. Despite being previously unknown, these distributions are attractive for numerous applications, some of which are discussed in this work.