Estimation in the pearson type 3 distribution

Abstract

Although the Pearson type 3 (P3) is one of the basic models in statistical hydrology, its use to model untransformed data has been restrained because of difficulties encountered in fitting this distribution by traditional methods. In this paper an adaptive estimation procedure of mixed moments for the P3 family is introduced which is based on several fractional moments of the exponentially transformed data and the mean of the original data. The procedure is easy to implement in small samples and is valid over the entire parameter space. Explicit formulae for the variances and covariances of parameter estimators and of the variance of the T-year event are derived. In addition, two variants of the new procedure are compared with two versions of the method of moments and a version of the method of conditional moments via Monte Carlo simulation. With samples generated from P3 populations, it is found that one of the variants of the new procedure is the best overall method in estimating 100-year flood events, and the other variant is best in estimating the median and 10-year low-flow events. The good performance of these two variants is also observed in samples generated from alternatives to P3 distributions. A modification of the procedure is also introduced and investigated when a prior assumption of positive skewness is adopted.