Here I show you how you can make a random Cauchy sample look like a Gaussian (and here is the accompanying paper with theory and methodology). The data is transformed by a non-linear, but bijective transformation – thus you can go back and forth between Cauchy and Gaussian-like.

library(LambertW) set.seed(10) nn <- 100 yy <- rcauchy(n = nn) normfit(yy) # definitely not Gaussian xx <- Gaussianize(yy, method="MLE") normfit(xx) # Gaussian # what does the Lambert W x Gaussian model look like? mod <- MLE_LambertW(yy, type="h") summary(mod) plot(mod)