Overview

This monograph provides a complete and comprehensive introduction to the theory of long-tailed and subexponential distributions in one dimension. New results are presented in a simple, coherent and systematic way. All the standard properties of such convolutions are then obtained as easy consequences of these results. The book focuses on more theoretical aspects. A discussion of where the areas of applications currently stand in included as is some preliminary mathematical material. Mathematical modelers (for e.g. in finance and environmental science) and statisticians will find this book useful.

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9781441994721

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From the reviews: The book An Introduction to Heavy-Tailed and Subexponential Distributions ... presents numerous ideas of 'heaviness' for probability distribution tails. It gives precise definitions to common terms such as heavy-tailed and long-tailed, as well as more esoteric terms such as subexponential or h-insensitive. ... This book is small, self-contained monograph. There are some examples and applications, but the emphasis is on basic properties and classification. (John D. Cook, The Mathematical Association of America, August, 2011) This monograph provides a comprehensive introduction to the theory of long-tailed and sub-exponential distributions. ... Every chapter ends with historical comments on the topics that it covers, and the book ends with a list of references. Most of the material covered is appearing for the first time in book form, and the book will serve as a valuable reference for researchers interested in tail properties of sums and maxima of independent random variables having long-tailed/sub-exponential distributions. (Sreenivasan Ravi, Mathematical Reviews, Issue 2012 f)

From the reviews: The book An Introduction to Heavy-Tailed and Subexponential Distributions ... presents numerous ideas of 'heaviness' for probability distribution tails. It gives precise definitions to common terms such as heavy-tailed and long-tailed, as well as more esoteric terms such as subexponential or h-insensitive. ... This book is small, self-contained monograph. There are some examples and applications, but the emphasis is on basic properties and classification. (John D. Cook, The Mathematical Association of America, August, 2011)

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