In many applications of hydrology, quantiles provide important insights in the statistical problems considered. In this paper, we focus on the estimation of multivariate quantiles based on copulas. We provide a nonparametric estimation procedure for a notion of multivariate quantiles, which has been used in a series of papers. These quantiles are based on particular level sets of copulas and admit the usual probabilistic interpretation that a p‐quantile comprises a probability mass p. We also explore the usefulness of a smoothed bootstrap in the estimation process. Our simulation results show that the nonparametric estimation procedure yields excellent results and that the smoothed bootstrap can be beneficially applied. The main purpose of our paper is to provide an easily applicable method for practitioners and applied researchers in domains such as hydrology and coastal engineering.

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Summary The emission requirements for jet engines are becoming more stringent and the combustion process determines pollutant emissions. Therefore, we model the distribution of fuel drops generated by a fuel injector in a jet engine, which can be assumed to be a five-dimensional problem in terms of drop size, x-position, y-position, x-velocity and y-velocity. The data are generated by numerical simulations of the fuel atomization process for several jet engine operating conditions. In combustion simulations, the variables are usually assumed to be independent at the start of the simulation, which is clearly not so as our data show. The dependence between some of the variables is non-monotone and asymmetric, which makes the modelling task difficult. Our aim is to provide a realistic parametric model for the dependence structure. For this, we employ vine copulas which provide a flexible way to construct a multivariate distribution function. However, we need to use non-standard bivariate copulas as building blocks. Using this copula representation enables us to create realistic samples of fuel spray droplets which improve the prediction of the combustion process and the pollutant emissions. Moreover, this approach is significantly faster than solving the set of differential equations describing fuel disintegration.

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