Comparison of methods for fitting data using Johnson translation distributions

The Johnson translation family of distributions provides a variety of distributional shapes for the modelling of empirical data that are readily used in simulation models. We compare a number of methods for estimating the parameters of these distributions, including moment matching (MM), least squares (ordinary- (OLS), weighted- (WLS) and diagonally weighted- (DWLS) least squares), and maximum likelihood (MLE). A sampling study is made to determine the properties of the fitted parameters and estimates based on the fitted parameters, such as the quantiles of the distribution. We restrict attention to the case that the analyst knows the correct distribution when fitting the parameters.