AUTHOR=Vélez Jorge I. , Correa Juan C. , Marmolejo-Ramos Fernando 

TITLE=A new approach to the Box–Cox transformation

JOURNAL=Frontiers in Applied Mathematics and Statistics

VOLUME=1

YEAR=2015

URL=https://www.frontiersin.org/journals/applied-mathematics-and-statistics/articles/10.3389/fams.2015.00012

DOI=10.3389/fams.2015.00012

ISSN=2297-4687

ABSTRACT=<p>We propose a new methodology to estimate λ, the parameter of the Box–Cox transformation, as well as an alternative method to determine plausible values for it. The former is accomplished by defining a grid of values for λ and further perform a normality test on the λ-transformed data. The optimum value of λ, say λ<sup>*</sup>, is such that the <italic>p</italic>-value from the normality test is the highest. The set of plausible values is determined using the inverse probability method after plotting the <italic>p</italic>-values against the values of λ on the grid. Our methodology is illustrated with two real-world data sets. Furthermore, a simulation study suggests that our method improves the symmetry, kurtosis and, hence, the normality of data, making it a feasible alternative to the traditional Box–Cox transformation.</p>