Log-Pearson Type III Distribution

Abstract

The log-Pearson type 3 (LP3) distribution has been one of the most frequently used distributions for hydrologic frequency analyses since the recommendation of the Water Resources Council (1967, 1982) of the United States as to its use as the base method. The Water Resources Council also recommended that this distribution be fitted to sample data by using mean, standard deviation and coefficient of skewness of the logarithms of flow data [i.e., the method of moments (MOM)]. A large volume of literature on the LP3 distribution has since been published with regard to its accuracy and methods of fitting or parameter estimation. McMahon and Srikanthan (1981) and Srikanthan and McMahon (1981) examined the applicability of LP3 distribution to Australian rivers and questioned the assumption of setting to zero the coefficient of skewness of logarithms of peak discharges that were not statistically different from zero. They evaluated the effect of sample size, distribution parameters and dependence on peak annual flood estimates. Gupta and Deshpande (1974) applied LP3 distribution to evaluate design earthquake magnitudes. Phien and Jivajirajah (1984) applied LP3 distribution to annual maximum rainfall, annual streamflow and annual rainfall. Wallis and Wood (1985) found, based on Monte Carlo experiments, that the flood quantile estimates obtained by using an index flood type approach with either a generalized extreme value distribution or a Wakeby distribution fitted by PWM were superior to those obtained by LP3 distribution with MOM -based parameters. This finding was challenged later by several investigators (Beard, 1986; Landwehr et al., 1986).