Logarithmic Lambert $\mathrm{W}\times {\cal F}$ random variables for the family of chi-squared distributions and their applications

TL;DR

This paper introduces a new class of logarithmic Lambert W random variables tailored for chi-squared distributions, enhancing the understanding and application of these variables in likelihood-based inference for normal data.

Contribution

It characterizes the log-Lambert W random variables for chi-squared distributions, a novel contribution to the statistical theory and inference methods.

Findings

Provides a new characterization of log-Lambert W variables for chi-squared distributions.

Facilitates improved likelihood-based inference for normal variables.

Enhances understanding of distributional properties relevant to statistical inference.

Abstract

We introduce a class of logarithmic Lambert W random variables for a specific family of distributions. In particular, we characterize the log-Lambert W random variables for chi-squared distributions which naturally appear in the likelihood based inference of normal random variables.