Statistical Model of Simulation

• In this chapter, we discuss some of the most commonly used statistical models.

• Motivation:
  • So far we used only the uniformly distributed random numbers. They only fit a fraction of the real applications.
  • We need other kind of statistical models to describe various types of applications.
  • These models can be used in other situations than simulation. But we discuss them in the context of simulation.

• There are two major categories of random numbers:discrete and continueous.

• The discrete distributions we will discuss inculde:
  1. Bernoulli distribution
  2. Binomial distribution
  3. Geometric distribution
  4. Poisson distribution

• Contineous distributions include:
  1. Uniform distribution
  2. Exponential distribution
  3. Gamma distribution
  4. Erlang distribution
  5. Normal distribution
  6. Weibull distribution
  7. Triangle distribution

• Note that here we discuss random variables that are discretely or contineously distributed. This doesn't have a direct connection to discrete simulation vs. contineous simulation where the concept is how the simulation clock is ticked.

• We will talk about some of the basics of probabilities first. Then we will discuss various distributions. Then we will study the Poisson process, a very important, yet relatively simple distribution.