Peak Flood Discharge Confidence Limits

Confidence limits along with a lower bound for the corresponding level of confidence are developed for evaluating the effect of the sampling error on flood risk evaluation from base-flow flood data. It is assumed that the number of flood peak occurrences is Poisson-distributed with exponentially distributed magnitudes. A confidence region is obtained for the Poisson and exponential distribution parameters from the asymptotic joint distribution of their maximum likelihood estimators. It is shown how this region can be used to obtain confidence limits for measures of risk which are calculated using the estimates. The limits are easy to calculate and, if desired, a graphical technique can be used. The technique is restricted, however, to situations where the base-flow record is sufficiently long so that the sampling distribution for the estimators can be approximated by a limiting normal distribution.