Filling the gap between point-in-time and extreme value distributions M´ ınguez, R., Guanche, Y., Jaime, F. F., M´ endez, F. J. & Tom´ as, A. Environmental Hydraulics Institute “IH Cantabria”, Universidad de Cantabria, Spain ABSTRACT: Engineering structures must satisfy different requirements during its life-cycle: construction, useful life and dismantling. The satisfaction of those requirements is checked by defining failure probabilities associated with the different ways in which the structure might fail, also known as limit states. Threshold or maximum allowed probabilities are defined by expert committees according to the consequences produced in case each limit state is trespassed. From the practical point of view, this distinction requires the characterization of both the point-in-time and extreme probability (right tail) distribution of all random variables involved, and the selection of the appropriate distribution depending on the limit state. However, there are still international code regulations and design standards that do not clarify this issue and might lead to get invalid designs from the engineering perspective. This paper provides a practical guide based on M´ ınguez, Guanche, & M´ endez (2012) work in order to: i) analyze if distinction between both distributions is relevant for each failure mode, ii) which distribution should be used, and iii) how to work with both distributions at the same time. In addition, an example of the importance of these considerations using the IEC international standards for the definition of design requirements for offshore wind turbines (IEC 61400-3) is given. 1 INTRODUCTION Engineering structures must satisfy several design conditions during its lifetime with a certain probabil- ity of failure. Those acceptable rates are established by codes and expert committees (Baker 1976, Lind 1976, Horne & H. 1977, ROM 0.0 2001) on the ba- sis of the consequences of failure for each limit state, and trying to counter-balance safety and costs (direct, societal and environmental). These different proba- bility thresholds encompass the consideration of dif- ferent probability distributions for agents, while ser- viceability or operating stop limit conditions depend on regular or mean values (point-in-time) of those agents, damage and ultimate limit states require ex- treme conditions or conditions in the right tail. Tra- ditionally, both problems are treated independently, which makes difficult to understand the link between point-in-time and extreme distributions and their im- plications from the practical point of view. There are several attempts in the literature to in- corporate the information from both distributions in the same probability model (mixture models), see for instance, Frigessi, Haug, & Rue (2002) ,Vaz de Melo Mendes & Freitas Lopes (2004), Behrens, Lopes, & Gamerman (2004), Tancredi, Anderson, & Ohagan (2006), Cai, Gouldby, Hawkes, & Dunning (2008), Furrer & Katz (2001), Solari (2011). How- ever, they are applied to specific distributions, and the parameter estimation is fuzzy, not providing a general framework to deal with this problem. Recently, M´ ınguez, Guanche, & M´ endez (2012) presented some findings about this issue, focusing on three aspects: i) the development of a Monte Carlo simulation method for reproducing both the point-in- time (mean values) and extreme value distributions of random variables involved, ii) presenting a graph- ical interpretation to merge both distributions on a compatible scale, and iii) providing new insights for the use of the point-in-time and extreme regimes si- multaneously within First-Order-Reliability methods (FORM). An example of this problem is shown using the sea level record at San Francisco (see Figure 1), where an- nual maxima are plotted using triangle marker spec- ifiers. This data set consists of an hourly time series of sea level in meters from January 1, 1901 to De- cember 31, 2003. The particular record used in this paper only contains information on storm surge lev- els. Astronomical tidal and mean sea levels have been removed from the initial data record for illustrative purposes. Fitting the storm surge sea level, the correspond- ing annual maxima, and exceedances over threshold u =0.446 m to three different parametric distribu- tions: i) a Gaussian Mixture with 4 components for the point-in-time distribution, ii) a generalized ex- treme value (GEV) model for the annual maxima, and