A Tractable Probability Distribution with Applications in Three-Dimensional Statistics

TL;DR

This paper introduces new, computationally tractable probability distributions for three-dimensional Gaussian and power norms, expanding the toolkit for statistical modeling in three-dimensional spaces.

Contribution

It presents novel families of distributions for 3D Gaussian and power norms, which are computationally tractable and previously unknown.

Findings

New distributions for 3D Gaussian norms introduced

Distributions are computationally tractable

Potential applications discussed

Abstract

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.