We describe a simple graphic, the "inverted q-q plot" that enables visualization of the monotonic function that transforms data to a desired target distribution. An important special case is use of the Box-Cox family to transform data to a normal distribution. Using this graphic, we develop a novel way to estimate parameters in a transformation; although slightly less efficient than using maximum likelihood, our approach can be advantageous in controlling the effect of outlying observations. We also describe how regression smoothers like LOESS can be used to form nonparametric transformations when a simple parametric family is not appropriate.
A Visualization of Transformations