exp [- {i¥e + i¥t— iv} (it, it, it ) dt,dt,dt 
exp |—{i¥e+ tit—i¥t]] exp [KGr.itit)] dt.dt.a 
exp [-i¥r—i¥r—i¥s+ K(it, it, it)| de,de,ar 
| ex [100 ~Y) it+(ko10—Y) it + (koo — Vit 
1 9 35) : x 50 
5 {ikooot? + Ko20t~ + Kooat “+ 2k1 ott + 2kio it t+ 2ko yt t } 
+> ae — (ity) (i) GEY") dt, di, di (12.154) 
< jtktm! 
Here j, k, and m are now positive integers whose sum is greater than 2. 
The relations between joint moment and joint cumulants are 
k100 = 4100 
ko10 = Ho10 
koo1 = Ho01 Ones) 
ko09 = variance of Y ve 
ko29 = variance of Y 
Koo2 = variance of Y. 
Nondimensionalizing the variables as follows 
1/2 
z=(Y- k1o0) kobe 
. 3 1/2 
Ba (Ve ain (12.156) 
Z = (¥—kookohp 
and 
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