The fundamentals of heavy-tails

Jayakrishnan Nair, Adam Wierman, Bert Zwart
2013 Performance Evaluation Review  
Heavy-tailed distributions Tutorial overview Heavy-tails are a continual source of excitement and confusion across disciplines as they are repeatedly "discovered" in new contexts. This is especially true within computer systems, where heavy-tails seemingly pop up everywhere -from degree distributions in the internet and social networks to file sizes and interarrival times of workloads. However, despite nearly a decade of work on heavy-tails they are still treated as mysterious, surprising, and
more » ... s, surprising, and even controversial. The goal of this tutorial is to show that heavy-tailed distributions need not be mysterious and should not be surprising or controversial. In particular, we will demystify heavytailed distributions by showing how to reason formally about their counter-intuitive properties; we will highlight that their emergence should be expected (not surprising) by showing that a wide variety of general processes lead to heavy-tailed distributions; and we will highlight that most of the controversy surrounding heavy-tails is the result of bad statistics, and can be avoided by using the proper tools. Intended audience The tutorial is aimed at students, researchers, and practitioners interested in learning how to rigorously think about heavy-tailed distributions. The assumed background is only a basic understanding of probability and statistics. References The organizers of this tutorial are in the process of writing a book on the topic of heavy-tails, and this tutorial is meant to provide a brief overview of the material to be covered in the forthcoming book.
doi:10.1145/2494232.2466587 fatcat:ytjiyb7rtzg3nm4d2wok4olq7m