Multivariate Distributions with Specified Marginals: Applications to Wind Engineering

Bounds on and approximations of the distribution of a non-Gaussian vector $\mathbf{X}$ specified partially by the marginal distributions $F_i$ of its coordinates $X_i$ or the marginal distributions $F_i$ and some information on the correlation structure of $\mathbf{X}$ are developed. These results are used to: (1) bound and approximate the distribution of the largest coordinate of $\mathbf{X}$ , that is, the random variable $Y={\max }_i\left\{X_i\right\}$ ; and (2) evaluate current practice in wind engineering based on models for directional and directionless wind speeds (that is, yearly maximum wind speeds recorded in several directions and irrespective of direction) that are postulated independently of each other. It is shown that, although current directional and directionless wind speed models are inconsistent with probability theory, they can deliver similar design wind speeds if calibrated to very long wind speed records but their predictions can differ significantly if based on typically available records.