Generalized Method of Moments Applied to LP3 Distribution

Abstract

The log-Pearson type 3 (LP3) distribution is recommended in the United States by the Water Resources Council (WRC) as the parent distribution to maximum annual flood series. The parameter estimation technique proposed for this distribution consists in applying a logarithmic transformation to the observed flood sample and then applying the method of moments to these logarithmic values using moments of order 1, 2, and 3 (mean, variance, and coefficient of skew) in log space. Other methods have been proposed which use only moments in real space such as the mean, variance, geometric mean, harmonic mean, etc. of the observed sample, or combination of moments in real and log space (method of “mixed moments”). There are many other versions of the method of moments which have yet to be explored and evaluated. To help motivate this kind of exploration, we derive a general formula for the variance of the \IT\N-year event \IX\dT\N obtained by a method called the Generalized Method of Moments (GMM) which combines any three moments of the LP3 distribution. We also present a special case of the GMM which we all the Sundry Averages Method (SAM) which uses the harmonic, geometric, and arithmetic means of the distribution.