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Using partial moments, the authors introduce a new toolbox of statistical tools. The advantage of using partial moments is that it is nonparametric and does not require the knowledge of the underlying probability function nor does it require a "goodness of fit" analysis. Partial moments provide us with cumulative density functions, probability density functions, linear correlation and regression analysis, nonlinear correlation and regression analysis, ANOVA, and ARMA/ARCH models. One major advantage with this work is that the partial moment methodology fully replicates linear conditions...