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Infinite Divisibility of Probability Distributions on the Real Line : Chapman & Hall/CRC Pure and Applied Mathematics - Fred W. Steutel

Infinite Divisibility of Probability Distributions on the Real Line

Chapman & Hall/CRC Pure and Applied Mathematics

Hardcover Published: 3rd October 2003
ISBN: 9780824707248
Number Of Pages: 550

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Infinite Divisibility of Probability Distributions on the Real Line reassesses classical theory and presents new developments, while focusing on divisibility with respect to convolution or addition of independent random variables. This definitive, example-rich text supplies approximately 100 examples to correspond with all major chapter topics and reviews infinite divisibility in light of the central limit problem. It contrasts infinite divisibility with finite divisibility, discusses the preservation of infinite divisibility under mixing for many classes of distributions, and investigates self-decomposability and stability on the nonnegative reals, nonnegative integers, and the reals.

Industry Reviews

"The two authors have come up with a rather complete, very detailed and self-contained survey of the state of the art around the theory and applications of univariate infinite divisibility. All important properties are collected [in this book]. An important plus for this book is the rich variety of examples throughout the whole text. The monograph will certainly become the standard reference work on this fundamental concept." - Short Book Reviews of the ISI

Introduction and Overviewp. 1
Introductionp. 1
Elementary considerations and examplesp. 2
Processes with stationary independent incrementsp. 6
Canonical representationsp. 11
The central limit problemp. 13
Other types of divisibilityp. 19
Notesp. 21
Infinitely Divisible Distributions on the Nonnegative Integersp. 23
Introductionp. 23
Elementary propertiesp. 25
Compound distributionsp. 30
Canonical representationp. 34
Compound-exponential distributionsp. 39
Closure propertiesp. 43
Momentsp. 46
Supportp. 50
Tail behaviourp. 54
Log-convexityp. 59
Examplesp. 65
Notesp. 75
Infinitely Divisible Distributions on the Nonnegative Realsp. 77
Introductionp. 77
Elementary propertiesp. 79
Compound distributionsp. 84
Canonical representationp. 89
Compound-exponential distributionsp. 99
Closure propertiesp. 103
Momentsp. 106
Supportp. 109
Tail behaviourp. 113
Log-convexityp. 116
Examplesp. 124
Notesp. 133
Infinitely Divisible Distributions on the Real Linep. 135
Introductionp. 135
Elementary propertiesp. 137
Compound distributionsp. 145
Canonical representationp. 151
Compound-exponential distributionsp. 169
Closure propertiesp. 175
Momentsp. 176
Supportp. 182
Tail behaviourp. 189
Log-convexityp. 201
Examplesp. 208
Notesp. 218
Self-Decomposability and Stabilityp. 221
Introductionp. 221
Self-decomposability on the nonnegative realsp. 224
Stability on the nonnegative realsp. 241
Self-decomposability on the nonnegative integersp. 246
Stability on the nonnegative integersp. 262
Self-decomposability on the real linep. 268
Stability on the real linep. 286
Self-decomposability and stability induced by semi-groupsp. 300
Examplesp. 308
Notesp. 325
Infinite Divisibility and Mixturesp. 327
Introductionp. 327
Two important types of mixturesp. 329
Mixtures of exponential distributionsp. 331
Mixtures of gamma distributionsp. 343
Generalized gamma convolutionsp. 349
Mixtures of Poisson distributionsp. 367
Mixtures of negative-binomial distributionsp. 378
Generalized negative-binomial convolutionsp. 387
Mixtures of zero-mean normal distributionsp. 394
Mixtures of sym-gamma distributionsp. 398
Generalized sym-gamma convolutionsp. 403
Examplesp. 409
Notesp. 422
Infinite Divisibility in Stochastic Processesp. 425
Introductionp. 425
First-passage times in Markov chainsp. 426
Waiting times in queueing processesp. 431
Branching processesp. 433
Renewal processesp. 439
Shot noisep. 449
Examplesp. 450
Notesp. 461
Prerequisites from probability and analysisp. 465
Introductionp. 465
Distributions on the real linep. 465
Distributions on the nonnegative realsp. 477
Distributions on the nonnegative integersp. 489
Other auxiliariesp. 498
Notesp. 502
Selected well-known distributionsp. 503
Introductionp. 503
Distributions on the real linep. 503
Distributions on the nonnegative realsp. 506
Distributions on the nonnegative integersp. 509
Notesp. 511
Bibliographyp. 513
Author indexp. 535
Subject indexp. 539
Notations and conventionsp. 545
Table of Contents provided by Ingram. All Rights Reserved.

ISBN: 9780824707248
ISBN-10: 0824707249
Series: Chapman & Hall/CRC Pure and Applied Mathematics
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 550
Published: 3rd October 2003
Publisher: Taylor & Francis Inc
Country of Publication: US
Dimensions (cm): 23.06 x 15.95  x 3.12
Weight (kg): 0.86
Edition Number: 1

Earn 1616 Qantas Points
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