Pearson Type III Data Models for Precipitation Data: New Maximum Likelihood Approach

A new formulation of the maximum likelihood (ML) equations for the Pearson Type III (PE3) distribution permits the parameters to be found as roots of a one-dimensional function. By contrast, the usual approach requires finding the roots of a two-dimensional function. Techniques for solving the one-dimensional function in an efficient manner are discussed and applied to precipitation data. Results comparing the new and the old ML approach demonstrate that the new approach finds significantly greater percentages of roots in samples from both weakly and highly skewed distributions. A method for approximating confidence bounds on the estimated parameters is discussed and results are displayed on likelihood profile plots. An experimental software product for PC's that allows a reader to test and apply the new approach, is available on the Internet.