A Bivariate Extreme Value Distribution for Reliability Assessment of Marine Structures

A bivariate Gumbel distribution is established based on transformation of an existing bivariate Rayleigh distribution. Application of this distribution in relation to reliability assessment of marine structures is subsequently addressed. Linear combinations of the two basic variables which are Gumbel distributed are further considered. The role of the Gumbel distribution in connection with reliability assessment of marine structures is discussed. Comparison with another class of bivariate Gumbel distributions (Gumbel Type A) is also made.

A Bivariate Extreme Value Distribution Applied to Flood Frequency Analysis

This article presents a procedure for use of the Gumbel logistic model to represent the joint distribution of two correlated extreme events. Parameters of the distribution are estimated using the method of moments. On the basis of marginal distributions, the joint distribution, the conditional distributions, and the associated return periods can be deduced. The applicability of the model is demonstrated by using multiple episodic flood events of the Harricana River basin in the province of Quebec, Canada. It is concluded that the model is useful for describing joint probabilistic behavior of multivariate flood events.