# Heavy-Tail Phenomena

## Probabilistic and Statistical Modeling

• Sidney I. Resnick
Textbook

1. Front Matter
Pages i-xix
2. ### Introduction

1. Pages 1-14
3. ### Crash Courses

1. Front Matter
Pages 15-15
2. Pages 17-38
4. ### Statistics

1. Front Matter
Pages 71-71
2. Pages 73-116
5. ### Probability

1. Front Matter
Pages 117-117
2. Pages 119-165
3. Pages 211-251
4. Pages 253-287
6. ### More Statistics

1. Front Matter
Pages 289-289
2. Pages 291-356
7. ### Appendices

1. Front Matter
Pages 357-357
2. Pages 359-361
3. Pages 363-375
8. Back Matter
Pages 377-404

### Introduction

This comprehensive text gives an interesting and useful blend of the mathematical, probabilistic and statistical tools used in heavy-tail analysis. Heavy tails are characteristic of phenomena where there is a significant probability of a single huge value impacting system behavior. Record-breaking insurance losses, financial returns, sizes of files stored on a server, transmission rates of files are all examples of heavy-tailed phenomena.

Key features:

Unique text devoted to heavy-tails.

The treatment of heavy tails is largely dimensionless.

The text gives attention to both probability modeling and statistical methods for fitting models. Most other books focus on one or the other but not both.

The book emphasizes the broad applicability of heavy-tails to the fields of finance (e.g., value-at- risk), data networks, insurance.

The presentation is clear, efficient and coherent and, balances theory and data analysis to show the applicability and limitations of certain methods.

Several chapters examine in detail the mathematical properties of the methodologies as well as their implementation in the Splus or R statistical languages.

The exposition is driven by numerous examples and exercises.

Prerequisites for the reader include a prior course in stochastic processes and probability, some statistical background, some familiarity with time series analysis, and ability to use (or at least to learn) a statistics package such as R or Splus. This work will serve second-year graduate students and researchers in the areas of operations research, statistics, applied mathematics, electrical engineering, financial engineering, networking and economics.

Sidney Resnick is a Professor at Cornell University and has written several well-known bestsellers: A Probability Path (ISBN: 081764055X), Adventures in Stochastic Processes (ISBN: 0817635912) and Extreme Values, Regular Variation, and Point Processes (ISBN: 0387964819).

### Keywords

Analysis Fitting Poisson process STATISTICA Time series data analysis electrical engineering hydrology modeling operations research point process stochastic process

#### Authors and affiliations

• Sidney I. Resnick
• 1
1. 1.School of Operations Research and Industrial EngineeringCornell UniversityIthacaUSA