Maximum Likelihood Method for Q-Q and P-P Plots

This method can be employed to determine parameter estimates for a distribution (see Quantile-Quantile Plots and Probability-Probability Plots). In order to estimate a distribution parameter, the maximum likelihood method uses a value in the parameter space that corresponds to the largest "likelihood" for the sample data (i.e., the value that makes the observed data most probable). Alternatively, you can use the Method of Matching Moments to estimate the parameters. For more information, see Hahn and Shapiro, 1994.