I'"(fn.«i5ln) = 0.25 (27a) 



I'^'i^nJ'^oi.n) = 0.50 (27b) 



I'''(fn.^^5^.n) = 0.75 (27c) 



156. These quartile directions are illustrated as vertical dashed lines 

 in Figure 9b for each of the two modes shown. The object in this definition 

 is to have a nearly exact analogy with the parameterization shown in Figure 8. 

 In this way, the shapes of individual modes in a multimodal distribution can 

 be compared with the shapes of unimodal distributions having similar para- 

 meters . 



167. Characteristic spread, asymmetry, and positioning parameters for 

 individual modes are derived from the representative directions in the same 

 way that Equations 17, 18, and 19 are defined. Directional spread for 

 frequency f^ and mode k is given by 



A^'"^' = e&l. - e^,\l, (28) 



Figure 9b illustrates these as double arrows between the 25- and 75 -percent 

 vertical dashed lines for each of the two modes shown. 



168. An asymmetry parameter for mode k and frequency f,, is given by 



<" = 1- ;i'r ' ;ir (^9) 



*■ "50%, n ■ "75%, n ■' 



and a positioning parameter is given by 



^^"^ = 2 (Si\ln + O'^Mn) (30) 



169. One set of these three parameters (or, equivalently , the three 

 characteristic angles) can be found for each of K modes for a directional 

 distribution along frequency line n . If the distribution is unimodal, 



K = 1 and Equations 28, 29, and 30 become identical with Equations 17, 18, 

 and 19, respectively. 



66 



