CONFIDENCE INTERVALS FOR FLOOD EVENTS UNDER A PEARSON 3 OR LOG PEARSON 3 DISTRIBUTION1

ABSTRACT: The Pearson type 3 (P3) and log Pearson type 3 (LP3) distributions are very frequently used in flood frequency analysis. Existing methods for constructing confidence intervals for quantiles (X_p) of these two distributions are very crude. Most of these methods are based on the idea of adjusting confidence intervals for quantiles Y_p of the normal distribution to obtain approximate confidence inervals for quantiles X_p of the P3/LP3 distribution. Since there is no theoretical reason why this “base” distribution, Y, should be taken to be normal, we search in the present study for the best possible base distribution for producing confidence intervals for P3/LP3 quantiles. We consider a group of base distributions such as the normal, log normal, Weibull, Gumbel, and exponential. We first assume that the skew coefficient, γ of X, to be known, and develop a method for adjusting confidence intervals for Y_p to produce approximate confidence intervals for X_p. We then compare this method (Method A) with another method (Method B) introduced by Stedinger. Simulation shows that the performance of each of these two methods depends on the base distribution Y that is being used, but as a whole, the normal distribution appears to be the best-fit distribution for producing confidence intervals for P3/LP3 quantiles when γ is assumed to be known. We then extend our method (Method A) to the more important case of unknown coefficient of skewness. It is shown that by taking Y to be Weibull, fairly accurate confidence intervals for P3/LP3 quantiles can be obtained for quite a wide range of sample sizes and coefficients of skewness commonly found in hydrology. The case of the P3 distribution with negative skewness needs further research.