$\text{for } i = 1, 2, \ldots$ Where there are 3 parameters to be chosen: a, c, and m:
- m > 0
- 0 < a < m
- $0 \leq c \lt m$
- $0 \leq X_0 \lt m$
Random number (u): $u_i = x_i / m$
Implementing in python:
def LCM(n, seed, a, c, m):
x = []
x.append(seed)
for i in range(1, n+1):
x.append((a*x[i-1]+c)%m)
u = np.array(x)/m
return (list(u))
LCM(n=8, seed=4, a = 13, c = 0, m = 64)
#returns
[0.0625, 0.8125, 0.5625, 0.3125, 0.0625,
0.8125, 0.5625, 0.3125, 0.0625]
Standard properties are: a = 1102515245, c = 12345, m = 2^32
Testing Uniformity