- 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:
- Bernoulli distribution
- Binomial distribution
- Geometric distribution
- Poisson distribution

- Contineous distributions include:
- Uniform distribution
- Exponential distribution
- Gamma distribution
- Erlang distribution
- Normal distribution
- Weibull distribution
- 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.

- Review of Terminology and Concepts
- Useful Statistical Models
- Discrete Random Variables
- Contineous Distributions