Laserfiche WebLink
<br />11). For nominal exceedance probabilities less than O.SO-t-floods above the median-the expected <br />probability exceeds the nominal probability. This bias is ,emoved by replacing kp by the frequency factor: <br /> <br />k' = t [(n +11) In] 0.5 (21) <br />p n-I. p , <br /> <br />in which tn -I. p is the Student-t value with exceedance probability p. The visible effect of this adjustment <br />is to increase the slope of the estimated frequency curve in proportion to the statistical variability of the <br />sample statistics. <br /> <br />This normal-population result is applied to the Bul\etin 17B-estimated Pearson Type III distribution <br />with mean, standard deviation, and skew coefficient, 111:, S, and Gw, by first looking up the normal <br />exceedance probability p' corresponding to k' and, secqnd, applying the Pearson Type III frequency <br />p , <br />factor, kG, p' having this skew coefficient and probability! to the sample mean and standard deviation, as <br />follows: 111: + s( kG ,p')' Of course, even this estimate, When evaluated for any particular sample, <br />normally will mtsre~esent the true p-probability flood. With respect to a number of samples, however, the <br />fraction of floods actually exceeding the estimated p-pro~ability floods will be correct. Nonetheless, the <br />Bulletin 17B guidelines specify that the basic flood frequ~ncy curve (without expected probability) is the <br />I <br />curve to be used for estimating flood risk and forming w~ighted averages of independent flood frequency <br />estimates. <br /> <br />Confidence Limits <br /> <br />Finally, one-sided confidence limits for the p-proba~ility flood are computed. A one-sided confidence <br />limit is a sample statistic-hence a random variable-ha~ing a specified probability of exceeding (or not <br />exceeding) a specified population characteristic. In the Bulletin 17B analysis, these statistics are of the form <br />X + K . S , where X a~d S are the sample mean and stan~ard deviation after all Bulletin I7B tests and <br />adjustruents and K is a confidence coefficient chosen to satisfy the following equation: <br /> <br />p {X + K . S > /.L + ky.p ( cr)} = a <br /> <br />(22) <br /> <br />In this equation, /.L, cr, and 'Y are the population mean, sta~dard deviation, and skew coefficient, and the <br />right-hand side of the inequality is the population p-prob~bility flood; these parameters are unknown and <br />I <br />the idea is to find a K-value such that X + K . S , which qan be computed from the sample, will almost <br />certainly be an upper (or lower) bound on this unknown pppulation characteristic. In any particular sample <br />the computed value X + K . S may fail to bound the pop,ulation characteristic, but, over a number of <br />samples, the specified fraction-a (or I-a)-will yield correct bounds. A value of close to unity yields <br />upper confidence limits and a value close to zero yields lower limits. In particular, the upper 9S-percent <br />confidence limit has a = 0.9S; the lower 9S-percent limit ras a = O.OS. The value of K is found by <br />rearranging the probability statement as follows: <br /> <br />{((/.L-X)/(cr/Jn)+Jn(ky,p)) r: }= <br />P (S/cr) , < .,Ill (K) a <br /> <br />(23) <br /> <br />PEAKFQ <br /> <br />13 <br /> <br />DRAFT .1/30/98 <br />