Solved – Normalizing skewness with the Power or Box-Cox Transformation

data transformationmomentsskewness

Suppose I have a random sample drawn from an arbitrary strictly positive continuous distribution. Suppose moreover that I want to use the Box-Cox transform to zero out the skewness. Is there an explicit solution to the required value of the exponent lambda that can be calculated as a function of the skewness or any other sample statistic, or is it necessary to find it through numerical methods?

I have revised this question in light of Glen's comment to respect the allowable range of the Box-Cox

Best Answer

According to this: https://medium.com/@kangeugine/box-cox-transformation-ba01df7da884 , $\lambda$ needs to be calibrated by cross-validation.