The parameters of principal and directional extrema in a marine environment are important in marine engineering design

especially for appropriate construction of oceanic platforms and other structures. When designing wave walls and break water structures

the orientation of the breakwater or seawall depends mainly on the direction of the strongest waves. However

the strength of the breakwater and the elevation of the seawall depend on the magnitude of the biggest wave height of the strongest waves. Thus

identification of directional extrema plays an important role in the design of wave factors. When calculating the directional extremum

different materials may require different specific computational methods

yet few theoretical studies have been conducted in this field of research. Based on multivariate extremum statistical theory

this paper utilizes a discrete random variable to build a joint probability model compounded by a discrete random variable and a multivariate continuous random variable. Furthermore

this paper provides the first investigation on the theories and methodologies to deduce wave directional extrema. The results provide tools for both creating the calculation method of the directional extremum value and providing the rational directional extremum parameters for marine engineering design.