Model inputs capture the environment of the problem



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Monte Carlo Simulation










Model inputs capture the environment of the problem

  • Model inputs capture the environment of the problem

  • The simulation model

    • Conceptual model: set of assumptions that define the system
    • Computer code: the implementation of the conceptual model
  • Outputs describe the aspects of system behaviour that we are interested in



Uniform Random numbers or pseudo-random numbers (PRN) are essentially independent random variables uniformly Distributed over the unit interval (0,1).

  • Uniform Random numbers or pseudo-random numbers (PRN) are essentially independent random variables uniformly Distributed over the unit interval (0,1).

  • ●The PRNs are good if they are uniformly distributed,

  • statistically independent and reproducible.



Generating a random sequence of numbers {X1,X2,…….,Xk} of length M over the interval [0,M-1]

  • Generating a random sequence of numbers {X1,X2,…….,Xk} of length M over the interval [0,M-1]

  • Xi=mod(AXi-1+C,M)

  • R=Xi/M

  • ♠♠♠ mod(b,M)=b-int(b/M)*M

  • ● Starting value X0 is called “seed”

  • ●M,A and C are nonnegative integers known

  • Modulus, multiplier and increment, respectively

  • ●M is must be prime number(2³¹-1,2-1,…..)





Classic Example







Hit and miss method











Sample Mean method

  • Rewrite

































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