2.4 The multiplicative congruential method
The multiplicative congruential random number generator is defined by
Xi = aXi-1 (mod m)
Illustration: Let a be 3 and m=102. X (mod 100) is the two least significant digits of X, when X is expressed in decimal form. Using the seed 11 we obtain
X 3X Recurrence graph
11 33 11 ->
33 99 33 ->
99 297 99 ->
97 291 97 ->
91 273 91 ->
73 219 73 ->
19 57 19 ->
57 171 57 ->
71 213 71 ->
13 39 13 ->
39 117 39 ->
17 51 17 ->
51 153 51 ->
53 159 53 ->
59 177 59 ->
77 231 77 ->
31 93 31 ->
93 279 93 ->
79 237 79 ->
37 111 37 ->
11
We thus obtain a sequence of 20 different numbers distributed as
Range frequency
0-19 4
20-39 4
40-59 4
60-79 4
80-99 4
which gives some indication of uniform distribution.
2.5 The mixed congruential method
The mixed congruential random number generator is defined by
Xi = aXi-1+c (mod m)
The multiplicative congruential generator is a special case of the mixed with c=0.