This paper construct a family of non-linearity tests based on the distance histogram C(m, ε) underlying Grassberger and Procaccias Correlation Dimension (CD), Brock, Dechert and Sheink-mans (BDS) statistic, Mizrachs Simple Non-Parametric Test (SNT) and Mayers Correlation Dimension Ratio (CDR). Two new elements are introduced. The Þrst is homogenizing the data to the uniform or to the normal...