Log-Pearson Type 3 distribution and its application in flood frequency analysis. I: Distribution characteristics

Since the adoption of the log-Pearson Type 3 (LP3) distribution by U.S. federal agencies, it has been widely used in hydrology, but its properties are not well understood. This paper explores the characteristics of the LP3 distribution in both real space and log space, and their relationship. Comparisons with U.S. flood data summaries reveal that the LP3 distribution provides a reasonable model of the distribution of annual flood series from unregulated watersheds for log space skews vertical bar gamma(x),vertical bar <= 1.414 (though vertical bar gamma(x)vertical bar <= 1 is more realistic), and for gamma(x)=0 with standard deviations in the range 0.1 to 1.0 with base-e natural logarithms (0.04 to 0.43 with base-10 common logarithms). L-moment ratio relationships for the LP3 distribution are also developed so they can be compared to summary statistics for a region, and to several other distributions frequently recommended for modeling hydrometeorological extremes.