17: Common Distributions (Extremistan)
"Most quantities of interest, most projections, most numerical assessments are not point estimates. Rather they are rough distributions — not always normal, sometimes bi-modal, sometimes exponential, sometimes something else." - John Allen Paulos"We must be careful not to confuse data with the abstractions we use to analyze them" - William James.Lecture outline: What are some commonly used distributions that apply to performance evaluation studies of computer networks?
1. Exponential distribution and generalizations (still in the realm of mild randomness)
Exponential distribution;
Gamma distribution;
Phase type distributions;
Hypoexponential and Hyperexponential distributions;
Weibull distribution;
Comparison between Gamma and Weibull distributions
2. Extremistan: long tailed distributions
Weibull distribution (a long-tailed distribution)
Power-law vs. Exponential decay
Heavy-tailed (Power-Law) vs. Long-tailed distributions
Pareto distribution (a heavy tailed distribution)
Lognormal distribution (another long-tailed distribution)
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:
“Fundamentals of Performance Evaluation of Computer and Telecommunication System”, by Obaidat and Boudriga; Chapter 10: “Commonly Used Distributions in Simulation and Their Applications”.