FITTING: A SUBROUTINE TO FIT FOUR-MOMENT PROBABILITY DISTRIBUTIONS TO DATA

Fitting is a Fortran subroutine that constructs a smooth, generalized four-parameter probability distribution model. It is fit to the first four statistical moments of the random variable X (i.e., average values of X, X2, X3, and X4). This distribution is said to be "generalized" in that it generalizes various conventional, standard two-parameter "parent" distribution models. The user may select here between Gaussian, Gumbel, or Weibull parent models. The generalized model is then produced from a cubic distortion of the parent model, calibrated to match the first four moments of the data. (Depending on the numerical values of the moments, an inverse cubic distortion is instead used in some cases.) This four-moment matching is intended to provide models that are more faithful to the data in the tail regions of interest.