Question

3. Considering random number generators, give short answers (a couple of words) for the following: (a) What advantage does an MLCG have over an LCG? (b) What is the primary advantage of combined MRG over the MLCG?
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Answer 1

Answer:

The advantages of using an LCG:

1. Very fast to implement

2. It requires no storage of the numbers, only the most recent value.

3.Replication: Using the same seed, you can generate exactly the same sequence again and again which is extremely useful when comparing alternative systems/models:

By using the same numbers you are reducing the variability of differences that would be caused by using different numbers; any difference in the comparisons is thus due to the inherent difference in the models themselves.

Multiplicative congruential generators, also known as Lehmer random number generators, is a type of linear congruential generator for generating pseudorandom numbers in U(0, 1)U(0, 1). The multiplicative congruential generator, often abbreviated as MLCG or MCG, is defined as a recurrence relation similar to the LCG with c = 0c = 0.

Xi+1=aXi mod mXi+1=aXi mod m

Unlike the LCG, the parameters aa and mm for multiplicative congruential generators are more restricted and the initial seed X0X0 must be relatively prime to the modulus mm (the greatest common divisor between X0X0 and mm is 0). The current parameters in common use are m = 231 − 1 = 2147483647m = 231 − 1 = 2147483647 and a = 75 = 16807a = 75 = 16807.