Confidence intervals of quantiles in hydrology computed by an analytical method

Fitting probability distributions to hydrologic data samples is widely used for quantile estimation purposes. The estimated quantile ((X) over cap (T) ) is related to a return period (T). The confidence interval associated wit h each of the estimates has been calculated empirically, up until now, supp osing that the quantile estimator is normally distributed. In this study, i t is shown that the confidence interval follows a normal distribution only in the central part of the distribution. The real confidence limits are com puted analytically, by defining and integrating the probability density fun ction of the confidence interval. The results with an important number of h ydrologic samples show that the upper confidence limits are significantly u nderestimated towards the tail of the distribution, when determined using t he normality approximation for the quantile estimator.