Acknowledgment of priority: Usage of the Lambert W function in statistics
Abstract
In my 2011 Annals of Applied Statistics article [Goerg (2011)] I wrote that "Whereas the Lambert W function plays an important role in mathematics, physics, chemistry, biology and other fields, it has not yet been used in statistics." This was incorrect. At the time of publication I was unaware of Stehl\'k (2003), who used the Lambert W function to derive the exact distribution of the likelihood ratio test statistic. He has also used it in more recent work such as Stehl\'k (2006), Stehl\'k et al. (2010), or Stehl\'k (2014) amongst others. While Stehl\'ik's use of the Lambert W function was focused on the distribution of the likelihood ratio test statistic, my work dealt with the modeling of skewed random variables and symmetrizing data using the Lambert W function as a variable transformation.