Simulation of Random Variables                                                                                              Print this page
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  Simulation of Random Variables

  • In many fields of science and engineering, computer simulation is used to study random phenomena in nature and the performance of an engineering system in a noisy environment. For example, we may study through computer simulation the performance of a communication receiver. Sometimes a probability model may not be analytically tractable and computer simulation is used to calculate probabilities.

  • The heart of all these applications is that it is possible to simulate a random variable with an empirical CDF or PDF that fits well with the theoretical CDF or PDF.
   Generation of Random Numbers

      Generation of random numbers means producing a sequence of independent random numbers with a specified CDF or PDF. All the random number generators rely on a routine to generate random numbers with the uniform PDF. Such routine is of vital importance because the quality of the generated random numbers with any other distribution depends on it. By the quality of the generated random numbers, we mean how closely the empirical CDF or PDF fits the true one.
      There are several algorithms to generate  random numbers. Note that these algorithms generate random number by a reproducible deterministic method. These numbers are pseudo random numbers because they are reproducible and the same sequence of numbers repeats after some period of count specific to the generating algorithm. This period is very high and a finite sample of data within the period appears to be uniformly distributed. We will not discuss about these algorithms. Software packages provide routines to generate such numbers.
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