Probabilistic description of metocean parameters by means of kernel density models 1. Theoretical background and first results

Abstract

In the present work a general kernel density model (KDM) has been introduced and assessed for the analytic representation of any empirical distribution function (univariate or multivariate) of metocean parameters. This model is based on the concept of kernel density function, which has been first introduced in the context of non-parametric discriminant analysis by Fix and Hodges [Nonparametric discrimination: consistency properties, 1951], and generalised to the multivariate case by Cacoulos [Ann Inst Math 18 (1966) 178]. In its standard form, the kernel density estimators are applied to given samples of observations, producing analytical (yet non-parametric) estimations of the unknown (underlying) probability density functions. Motivated by the fact that, in many practical applications, metocean data are available only in the form of histograms (grouped data), the present KDM is implemented in a way permitting to obtain analytical estimates of the underlying probability distributions on the basis of grouped data. The main features of the proposed KDM are: (i) it can treat multivariate data with very reasonable computational cost, (ii) it is flexible enough to represent quite general distribution patterns both in the univariate and in the multivariate case, (iii) with an appropriate selection of the bandwidth, results in very satisfactory representations, avoiding local pathologies, (iv) it is marginally consistent, i.e. any marginal distribution calculated by integration from the multivariate model is identical with the corresponding marginal KDM, obtained directly from the marginal data. First numerical results are presented herein, showing that the performance of the present model is very satisfactory for all the wave parameters studied, univariate, bivariate, the trivariate ( H S, T m, Θ m), and conditionals. A more detailed investigation, also including applications to other metocean parameters, will be presented as a second part.