An Introduction to Heavy-Tailed and Subexponential Distributions

1. Front Matter

   Pages i-xi

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2. Introduction

   • Sergey Foss, Dmitry Korshunov, Stan Zachary

   Pages 1-6

3. Heavy-Tailed and Long-Tailed Distributions

   • Sergey Foss, Dmitry Korshunov, Stan Zachary

   Pages 7-42

4. Subexponential Distributions

   • Sergey Foss, Dmitry Korshunov, Stan Zachary

   Pages 43-74

5. Densities and Local Probabilities

   • Sergey Foss, Dmitry Korshunov, Stan Zachary

   Pages 75-102

6. Maximum of Random Walk

   • Sergey Foss, Dmitry Korshunov, Stan Zachary

   Pages 103-143

7. Back Matter

   Pages 145-157

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Heavy-tailed probability distributions are an important component in the modeling of many stochastic systems. They are frequently used to accurately model inputs and outputs of computer and data networks and service facilities such as call centers. They are an essential for describing risk processes in finance and also for insurance premia pricing, and such distributions occur naturally in models of epidemiological spread. The class includes distributions with power law tails such as the Pareto, as well as the lognormal and certain Weibull distributions.

 

One of the highlights of this new edition is that it includes problems at the end of each chapter. Chapter 5 is also updated to include interesting applications to queueing theory, risk, and branching processes. New results are presented in a simple, coherent and systematic way.

Graduate students as well as modelers in the fields of finance, insurance, network science and environmental studies will find this book to be an essential reference.

• environmental modeling
• financial modeling
• lognormal distribution
• long-tailed distribution
• pareto distribution

• , Department of Actuarial Mathematics, Heriot-Watt University, Riccarton, Edinburgh, United Kingdom

  Sergey Foss

• Russian Academy of Sciences, Sobolev Institute of Mathematics of the, Novosibirsk, Russia

  Dmitry Korshunov

• , Department of Actuarial Mathematics and, Heriot-Watt University, Riccarton, Edinburgh, United Kingdom

  Stan Zachary

Sergey Foss is a professor at Heriot-Watt University, Edinburgh, UK. Dmitry Korshunov is a professor at the Sobolev Institute of Mathematics of the Russian Academy of Sciences, Novosibirsk, Russia. Stan Zachary is a professor at Heriot-Watt University, Edinburgh, UK.