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^_T) is related to a return period (T). The confidence interval associated with each of the estimates has been calculated empirically, up until now, supposing that the quantile estimator is normally distributed. In this study, it is shown that the confidence interval follows a normal distribution only in the central part of the distribution. The real confidence limits are computed analytically, by defining and integrating the probability density function of the confidence interval. The results with an important number of hydrologic samples show that the upper confidence limits are significantly underestimated towards the tail of the distribution, when determined using the normality approximation for the quantile estimator.