PROBABILITY PLOT GOODNESS-OF-FIT AND SKEWNESS ESTIMATION PROCEDURES FOR THE PEARSON TYPE-3 DISTRIBUTION

Uniform flood frequency guidelines in the United States currently recommend fitting a Pearson (P3) distribution to the logarithms of annual maximum flood flows. As a result, a plethora of procedures have been recommended for obtaining unbiased plotting positions and unbiased estimates of the skew coefficient and for inverting the cumulative distribution function of a P3 variate. These developments are precisely the ingredients required for the construction of P3 probability plots. Using Monte Carlo simulation, we develop a probability plot correlation coefficient (PPCC) hypothesis test for the P3 distribution. Power studies are performed to evaluate the ability of the test to discriminate among competing distributional alternatives and to enhance our understanding of why the P3 distribution often appears to provide such a good fit to observed flood flow data. A new estimator of the skew coefficient is presented which, unlike the biased and unbiased moment estimators, is unbounded and has significantly lower root mean square error than the moment estimators for highly skewed samples.