Poisson-Gumbel Mixed Compound Distribution and its ap-plication

Abstract

With the development of offshore engineering, the joint probability study for extreme sea environments has been a subject of increasing interest for both mathematicians and engineers. However, the conventional multivariate probability distribution models do not describe the distribution of the occurrences of extreme sea states induced by typhoon, hurricane or winter storm, and thus fail to reflect the probability characteristics of sea environments in all the aspects. Extreme sea environments are typically to be found in storms like typhoon, and the occurrences of such storms in certain sea areas, varying from year to year, may be fitted to a discrete distribution. By compounding the discrete distribution with a bivariate continuous distribution of two extreme sea environments, a new kind of distribution — Bivariate Compound Extreme Value Distribution (BCEVD) is obtained in this note. This study proposes Poisson-Gumbel Mixed Compound Distribution, one of the particular forms of BCEVD, and gives an example of its application by using it to compute the joint distribution of wind velocities and wave heights and to estimate the 100-year return level, based on the 20-year wind and wave data in the East China Sea. The results show the advantage of PGMCD model in its stable results and simple use.