149. The asymmetry parameter is most meaningful in unimodal directional 

 distributions or in isolated modes of multimodal distributions (described 

 below). In this report, A^ is used to group directional distributions with 

 similar shapes, as discussed in Part IX. 



150. A third parameter, also used in geometric comparisons, is a 

 positioning parameter determined from the mean of ^25% n ^^^ ^75% n • Called 

 6^ , it is given by 



^n = 2(^25%,n + «75%,n) (19) 



This parameter is used in Part IX to translate distributions along the 

 direction axis so that composite distributions can be constructed. For 

 distributions with the same spread parameter, it ensures that 25- and 75- 

 percent angles will align for all members of a composite and consequently 

 allows intercomparison of directional distribution shapes having constant 

 spread. Note that 9^ is used as a characteristic direction for reposition- 

 ing data on the direction axis. It is not the same as peak direction ^ , 

 which is the direction of the maximum of a distribution function. 



Some Bulk Spreading Parameters 



151. The parameters given by Equations 17, 18, and 19 are all specific 

 to distributions at a given frequency within a frequency-direction spectrum. 

 To characterize an entire frequency- direction spectrum, some measure of the 

 bulk or overall properties of the spectrum must be used. In this report, two 

 bulk spreading parameters are considered. One is deduced from the integrated 

 direction spectrum 5(9^) in the same way that A^j^ was found from 

 S(f^,6^) . The other is a spectrally weighted sum of the set of A9^ found 

 from a given frequency-direction spectrum. 



152. A spread parameter based on S(d^) is considered first. The IDS 

 is given by Equation 9. The area under this curve is, from Equation 12, one- 

 sixteenth H^o . A cumulative distribution can be constructed from S(^j„) by 

 the expression 



I(«j) = I TTfTlT d^ (20) 



60 



