Format:
1 online resource (132 pages)
ISBN:
9781441994738
Series Statement:
Springer Series in Operations Research and Financial Engineering Ser. v.38
Content:
This book offers a comprehensive introduction to the theory of long-tailed and subexponential distributions in one dimension, presenting new results in a simple, coherent and systematic manner that obtains the standard properties of such convolutions.
Content:
Intro -- An Introduction to Heavy-Tailed and Subexponential Distributions -- Preface -- Contents -- Notation and Conventions -- Chapter 1 Introduction -- Heavy-Tailed Distributions -- Long-Tailed Distributions -- Subexponential Distributions -- Example: The Weibull Distribution -- Chapter 2 Heavy-Tailed and Long-Tailed Distributions -- 2.1 Heavy-Tailed Distributions -- 2.2 Characterisation of Heavy-Tailed Distributions in Terms of Generalised Moments -- 2.3 Lower Limit for Tails of Convolutions -- 2.4 Long-Tailed Functions and Their Properties -- 2.5 Long-Tailed Distributions -- 2.6 Long-Tailed Distributions and Integrated Tails -- 2.7 Convolutions of Long-Tailed Distributions -- 2.8 h-Insensitive Distributions -- 2.9 Comments -- Chapter 3 Subexponential Distributions -- 3.1 Subexponential Distributions on the Positive Half-Line -- 3.2 Subexponential Distributions on the Whole Real Line -- 3.3 Subexponentiality and Weak Tail-Equivalence -- 3.4 The Class S* of Strong Subexponential Distributions -- 3.5 Sufficient Conditions for Subexponentiality -- 3.6 Conditions for Subexponentiality in Terms of Truncated Exponential Moments -- 3.7 S Is a Proper Subset of L -- 3.8 Does FS Imply That FIS? -- 3.9 Closure Properties of the Class of Subexponential Distributions -- 3.10 Kesten's Bound -- 3.11 Subexponentiality and Randomly Stopped Sums -- 3.12 Comments -- Chapter 4 Densities and Local Probabilities -- 4.1 Long Tailed Densities and Their Convolutions -- 4.2 Subexponential Densities on the Positive Half-Line -- 4.3 Subexponential Densities on the Real Line -- 4.4 Sufficient Conditions for Subexponentiality of Densities -- 4.5 -Long-Tailed Distributions and Their Convolutions -- 4.6 -Subexponential Distributions -- 4.7 -Subexponential Distributions on the Real Line -- 4.8 Sufficient Conditions for -Subexponentiality.
Note:
Description based on publisher supplied metadata and other sources
Additional Edition:
9781441994721
Additional Edition:
Erscheint auch als Druck-Ausgabe 9781441994721
Language:
English
