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Appendix F: Miscellaneous
FĆ6
AWG2021 User Manual
Random (rnd) Function
A random number generation algorithm uses an uniform distribution random
generation routine and the central-limit theorem to derive Gaussian distribution
random numbers.
Central-limit theorem: when the independent random variables X
1, X2..., and Xn
conform to an identical random distribution, the mean and variance of x = (X1 +
X
2 +... + Xn)/n are given as follows:
E(n) + m V(n) + s
2
ńn
Even if the initial random distribution is not normal, if a reasonably large value
for n is used, the arithmetical mean x of a considerably large number of variables
will be close to the normal distribution.
In actuality, 12 is used for n, uniform random numbers are accumulated n times
and their arithmetical mean is derived as the ultimate Gaussian distribution
random number.
The following algorithm is used to generate uniform distribution random
numbers:
seed [n] + (253.0 seed [n–1] ) 1.0) mod 16777216
ran + seed [n] ń16777216