Simulating Univariate and Multivariate Nonnormal Distributions through the Method of Percentiles

The proposed method is used primarily when (1) conventional (or L ) moment-based estimators such as skew (or L -skew) and kurtosis (or L -kurtosis) are unknown or (2) data are unavailable but percentiles are known (e.g., standardized test score reports).

The proposed transformation also has the advantage that solutions to polynomial coefficients are available in simple closed form and thus obviates numerical equation solving. A procedure is also described for simulating power method distributions with specified medians, inter-decile ranges, left-right tail-weight ratios (skew function), tail-weight factors (kurtosis function), and Spearman correlations. The Monte Carlo results presented in this study indicate that the estimators based on the method of percentiles are substantially superior to their corresponding conventional product-moment estimators in terms of relative bias.