Abstract
This work aims at deriving the most probable extreme response of highly nonlinear systems under random excitations based on a collection (ensemble) of small size samples by using order statistics in combination with non-parametric statistical inference methods (SIMs). The resulting scheme essentially consists of the r-largest Order Statistics (r-LOS) model and the (Delete-d) Jackknife or Bootstrap non-parametric, resampling methods. Using the r-LOS model when dealing with relatively small size samples, more information from the collected set of extremes per sample can be accrued as opposed to the common engineering practice of employing just the single highest extreme per sample, i.e., Block-Maxima approach.
On the other hand, SIMs, with the aid of resampling with or without replacement, can further enhance this information using artificially created ensembles. As a result, from the ensembles produced via resampling, quantile levels and distribution parameters such as shape, scale and location become new random variables. With the aid of these new distributions, the probability of extremes can be explained better in terms of both sample size, i.e., number of realizations and number of largest extremes per sample.
Due to data availability, a direct application-example for the illustration of the merits of this novel approach is the determination of the most-probable maximum of experimental green water related extreme loads. Using the proposed approach, the statistical attributes of recorded extremes and distribution-fit parameters can be assessed w.r.t:
a. the number of realizations,
b. the number of largest extremes per realization,
c. all possible combinations of a and b.
