Response to "Discussion of 'Modelling significant wave height distributions with quantile functions for estimation of extreme wave heights' [Ocean Engneering 54 (2012) 119–131]" by Zai-Jin You and David Callaghan

Abstract

The discussers have commented on the reference paper, discussing would be used and compared as done for example in Guedes various questions that include the method of quantiles, the characteristics of the data sets used in the examples and the conclusion about the choice among the various quantile distributions. The authors agree that whenever there is a distribution that has an analytical expression for its distribution F(x), the quantile function Q(p) can be derived from it and both describe the probabilistic nature of the variable x. In fact, when both can be derived explicitly it is equivalent to use one or the other to extreme value predictions. It is then a matter of taste the choice of one or the other. This is already stated in the original paper, where it is indicated that the purpose of presenting the quantile functions is exactly to suggest an alternative and equivalent method to determine extremes. However in cases inwhich F(x) does not have a closed form, then Q(p) should be used for extreme value analysis as the discussers also state. This would then be an advantage of using the quantile functions because in most cases what is available is a data set from which inferences are made for a F(x). This means that in practice an analytical expression of F(x) is not available, although an analytical expression might be adopted to model the data. The discussers then go on to comment on the case studies used for the demonstration of the application of the method. They specifically comment on the choice of daily maxima, which was done to reduce the size of the data set and the correlation among data. The objective of the paper was to propose the quantile functions and to demonstrate how they could be applied. The objective was not to determine the extreme value significant wave heights at a particular location. If that would have been the case indeed more care would be given to choose a data set with less correlation between the data as discussed for example in Ferreira and Guedes Soares (2000) and also several methods