Assume that I have a variable whose distribution is skewed positively to a very high degree, such that taking the log will not be sufficient in order to bring it within the range of skewness for a normal distribution. What are my options at this point? What can I do to transform the variable to a normal distribution?
Try straight Box-Cox transform as per Box, G. E. P. and Cox, D. R. (1964), “An Analysis of Transformations,” Journal of the Royal Statistical Society, Series B, 26, 211–234. SAS has the description of its loglikelihood function in Normalizing Transformations, which you can use to find the optimal λ parameter, which is described in Atkinson, A. C. (1985), Plots, Transformations, and Regression, New York: Oxford University Press.
It’s very easy to implement it having the LL function, or if you have a stat package like SAS or MATLAB use their commands: it’s boxcox command in MATLAB and PROC TRANSREG in SAS.
Also, in R this is in the MASS package, function boxcox().