engleski

Sensitivity to correlation in multivariate models

The paper presents some aspects of the sensitivity analysis within the multivariate distribution models. The procedures are provided for engineering problems based on Nataf model, involving marginal distributions of the random variables and the correlations between them. The sensitivities are considered via derivatives with respect to the correlation coefficients of the terms used in the transformation of variables. First, the terms for the derivatives of the Nataf correlation coefficients with respect to given correlation coefficients are presented. Next, the derivatives of the transformations between the random variables are given. The Cholesky decomposition and the spectral decomposition are applied. The derivatives of the Cholesky decomposition are obtained in the form of a recursive scheme. The derivatives of the eigenvalues and eigenvectors are obtained by perturbation method. In addition, a comprehensive method for the derivatives of the distances and of the angles are given. Finally, numerical examples are attached to illustrate the presented computational procedures.

ship concept design; sensitivity analysis; correlation coefficients; eigenvalues; multivariate models; NATAF - model

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