Generalized modulus power transformations

Several power transformations proposed in the past are examined to find out the type of distributions that they can normalize, and a general family of transformations "the Generalized Modulus Power Transformation- (GEMPT), is proposed, The GEMPT will remove skewness and kurtosis and induce normality from a broad class of distributions, which we investigate, implying certain limitations for all power transformations. The use of GEMPT is illustrated and shown to iead to a better approximation to a normal distribution in an example in which the response is expected to follow a rectangular hyperbola.