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.

翻译：本文提出并刻画了一类新的连续概率分布族，适用于三维随机空间中的范数分布，具体针对三个非零均值随机高斯变量的欧几里得范数。该分布定义在半无限区间$[0,\infty)$上，以其计算上的可处理性而著称。在此基础之上，我们还引入了另一类适用于三维随机空间中幂分布的连续概率分布族。尽管这些分布此前未被认知，但它们因在众多应用场景中的优势而具有吸引力，本文讨论了其中若干应用。