16: Common Distributions (Mediocristan)

"The probable is what usually happens" - Aristotle."Question: Why did you use the Gaussian assumption? Answer. Because it’s the normal assumption!", Overheard at a conference — S. Pasupathy (1989).Lecture outline: What are some commonly used distributions that apply to performance evaluation studies of computer networks?

1. How are distributions distinguished?

Symmetric or skewed?

Heavy tailed?

Mediocristan vs. Extremistan

Distribution parameters

2. Light tailed (mild randomness) distributions

Discrete distributions:

Uniform, Bernoulli, Binomial, Negative Binomial, Geometric, Poisson Distributions

Continuous distributions:

Normal distributions

(Another very important continuous distributions, the exponential distribution [which is still in the realm of mild randomness], will be covered at the start of next lecture. We will also cover its generalizations.)

Primary reference for this lecture:

“The Art of Computer Systems Performance Analysis: Techniques for Experimental Design, Measurement, Simulation, and Modeling” by Raj Jain; Chapter 29: “Commonly Used Distributions”.

Secondary references for this lecture:

1. “Fundamentals of Performance Evaluation of Computer and Telecommunication System”, by Obaidat and Boudriga; Chapter 10: “Commonly Used Distributions in Simulation and Their Applications”.

2. Compendium of Probability Distributions, McLaughlin (Link)

3. "Modern Engineering Statistics", by Thomas Ryan, Chapter 3.