Box-Cox Transformations - 60 Years After

Music City Center 

It was in 1964 that George Box and David Cox published a seminal paper on what now universally labeled as Box-Cox transformation. For a given random variable X > 0, Box and Cox proposed a power transformation of X, which is normally distributed after the transformation. The classical log transformation is a power tranformation in the limit. We query whether the proposed transformation can ever be normally distributed. We demonstrate that it cannot except in the limiting case. We modify the Box-Cox transformation and show that the transformed X now could normally be distributed. The new transformation gives rise to a new class of distributions on the positive real line joining the well-knowm distribitions such as weibull, lognormal, gamma, gumbel, etc.

Order Statistics

Optimization

Beta Distribution

Winning Probability

Game Show

Expectation 

Section on Teaching of Statistics in the Health Sciences