Simulation and modeling - Old Questions

The congruence method (linear congruential method) produces a sequence of integers X₁, X₂, X₃,.......between zero and m-1 according to the following recursive relationship:

• The initial value X₀ is called the seed;
• a is called the constant multiplier;
• c is the increment
• m is the modulus

The selection of a, c, m and X₀ drastically affects the statistical properties such as mean and variance, and the cycle length.

Case 1:

     When , the form is called the mixed congruential method.

Case 2:
    When c = 0, the form is known as the multiplicative congruential method.

Case 3:

    When a = 1, the form is known as additive congruential method.

The random numbers corresponding to each random integer can be obtained as:                                        

          R_i = X_i/m, for i = 0, 1, 2, 3, …………..