Logarithmic Lambert $\mathrm{W}\times {\cal F}$ random variables for the   family of chi-squared distributions and their applications
  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. 
Viktor Witkovsk\'y, Gejza Wimmer, Tomy Duby
math.ST stat.TH