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# 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.

Subsections

Next: Review of Terminology and Up: Simulation CSCI 6337 Previous: References
Meng Xiannong 2002-10-18