| Abstract: | ABSTRACT: A simple simulation type approach and a statistical method are proposed for determining the confidence interval of the T‐year frequency rainfall percentiles (or precipitation extremes) for generalized extreme value (GEV) distributions. The former method is based on the Monte Carlo testing procedure. To generate realizations, the covariance structure of the three parameters of GEV is investigated using an observed information matrix of the likelihood function. For distributions with realistic parameters, the correlation between the location and the scale parameters is practically constant when the shape parameter varies around values close to its optimal value. The latter method is based on likelihood ratio statistics. In the case where the joint confidence surface for shape parameters and estimates is plotted with lines of best estimates, the region where the estimated best percentile value can be chosen as a possible estimate is part of the joint confidence surface. The projection of this bounded region on axis of percentile is defined as the effective confidence interval in this research. The use of this effective interval as the confidence interval of the percentile of T‐year frequency rainfall is particularly recommended because it is stable for T and it reflects variations in all three parameters of GEV appropriately. |
