  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.
