Bivariate distribution with two-component extreme value marginals to model extreme wind speeds

C. ESCALANTE SANDOVAL

Abstract

The bivariate logistic model with two-component extreme value marginal distributions (BTCEV) is applied to provide a regional at-site wind speed estimate. The maximum likelihood estimators of the parameters were obtained numerically by using a multivariable constrained optimization algorithm. A total of 45 sets of largest annual wind speeds gathered of stations located in The Netherlands were selected to apply the model. Results were compared with those obtained by the univariate distributions: Gumbel (G), Generalized Extreme Value (GEV), Reverse Weibull (RW) and two-component extreme value (TCEV); the bivariate distributions with marginals G, GEV and RW; and three regional methods: station-year, index flood (index-wind) and L-moments. In general, a significant improvement occurs, measured through the use of a goodness-of-fit test, when estimating the parameters of the marginal distribution with the bivariate distributions instead of its univariate and regional counterpart, and differences between at-site and regional at-site design events can be significant as return period increases. Results suggest that it is very important to consider the bivariate joint estimation option when analyzing extreme wind speeds, especially for short samples.

Keywords

Wind speed frequency analysis, bivariate extreme value distribution, maximum likelihood parameter estimation, goodness-of-fit

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