A k-sample homogeneity test: the Harmonic Weighted Mass index

We propose a quantification of the p-p plot that assigns equal weight to all distances between the respective distributions: the surface between the p-p plot and the diagonal. This surface is labeled the Harmonic Weighted Mass (HWM) index. We introduce the diagonal-deviation (d-d) plot that allows the index to be computed exactly under all circumstances. This two-dimensional d-d plot accommodates a straightforward extension to the k-sample HWM index, with k > 2. A Monte Carlo simulation based on an example involving long-term sovereign credit ratings illustrates the power of the HWM test.