2r 0.1 



-Experimental Data 



12,365 observations each 

 of which feptescnts a 

 given sea state. 



H. 



12 16 



Significant Wave Height, feet 



Figure 2a - Distribution Function 



STATISTICAL BACKGROUND 



The wave heights, ship motions, and hull bending moments experienced under a given 

 set of conditions will be described or specified in terms of their distribution patterns or, math- 

 ematically speaking, their distribution functions. 



For illustrative purposes, consider one of the variables, for example, wave height. All 

 wave heights are considered to be members of a statistical "population." The distribution 

 function (d,f.) of wave heights indicates the relative probability p{x) of encountering a wave 

 of a given height as a function of that height. Figure 2a illustrates this distribution function. 

 (Similar illustrations are given for the ship motions in Figures 3 through 6.) The area under 

 the curve up to a value x- is the integral of the d.f. up to the value x= x-; it is equal to the 

 fraction of all members of the population of wave heights which have a height less than x^. 



