Generalized Gamma Convolutions and Related Classes of Distributions and Densities PDF Download
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Author: Lennart Bondesson
Publisher: Springer Science & Business Media
ISBN: 1461229480
Category : Mathematics
Languages : en
Pages : 184
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Book Description
Generalized Gamma convolutions were introduced by Olof Thorin in 1977 and were used by him to show that, in particular, the Lognormal distribution is infinitely divisible. After that a large number of papers rapidly appeared with new results in a somewhat random order. Many of the papers appeared in the Scandinavian Actuarial Journal. This work is an attempt to present the main results on this class of probability distributions and related classes in a rather logical order. The goal has been to be on a level that is not too advanced. However, since the field is rather technical, most readers will find difficult passages in the text. Those who do not want to visit a mysterious land situated between the land of probability theory and statistics and the land of classical analysis should not look at this work. When some years ago I submitted a survey to a journal it was suggested by the editor, K. Krickeberg, that it should be expanded to a book. However, at that time I was rather reluctant to do so since there remained so many problems to be solved or to be solved in a smoother way than before. Moreover, there was at that time some lack of probabilistic interpretations and applications. Many of the problems are now solved but still it is felt that more applications than those presented in the work could be found.
Author: Lennart Bondesson
Publisher: Springer Science & Business Media
ISBN: 1461229480
Category : Mathematics
Languages : en
Pages : 184
Get Book Here
Book Description
Generalized Gamma convolutions were introduced by Olof Thorin in 1977 and were used by him to show that, in particular, the Lognormal distribution is infinitely divisible. After that a large number of papers rapidly appeared with new results in a somewhat random order. Many of the papers appeared in the Scandinavian Actuarial Journal. This work is an attempt to present the main results on this class of probability distributions and related classes in a rather logical order. The goal has been to be on a level that is not too advanced. However, since the field is rather technical, most readers will find difficult passages in the text. Those who do not want to visit a mysterious land situated between the land of probability theory and statistics and the land of classical analysis should not look at this work. When some years ago I submitted a survey to a journal it was suggested by the editor, K. Krickeberg, that it should be expanded to a book. However, at that time I was rather reluctant to do so since there remained so many problems to be solved or to be solved in a smoother way than before. Moreover, there was at that time some lack of probabilistic interpretations and applications. Many of the problems are now solved but still it is felt that more applications than those presented in the work could be found.
Author: Lennart Bondesson
Publisher: Springer
ISBN: 9780387978666
Category : Mathematics
Languages : en
Pages : 0
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Book Description
Generalized Gamma convolutions were introduced by Olof Thorin in 1977 and were used by him to show that, in particular, the Lognormal distribution is infinitely divisible. After that a large number of papers rapidly appeared with new results in a somewhat random order. Many of the papers appeared in the Scandinavian Actuarial Journal. This work is an attempt to present the main results on this class of probability distributions and related classes in a rather logical order. The goal has been to be on a level that is not too advanced. However, since the field is rather technical, most readers will find difficult passages in the text. Those who do not want to visit a mysterious land situated between the land of probability theory and statistics and the land of classical analysis should not look at this work. When some years ago I submitted a survey to a journal it was suggested by the editor, K. Krickeberg, that it should be expanded to a book. However, at that time I was rather reluctant to do so since there remained so many problems to be solved or to be solved in a smoother way than before. Moreover, there was at that time some lack of probabilistic interpretations and applications. Many of the problems are now solved but still it is felt that more applications than those presented in the work could be found.
Author: Albert W. Marshall
Publisher: Springer Science & Business Media
ISBN: 0387684778
Category : Technology & Engineering
Languages : en
Pages : 785
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Book Description
This book is devoted to the study of univariate distributions appropriate for the analyses of data known to be nonnegative. The book includes much material from reliability theory in engineering and survival analysis in medicine.
Author: Fred W. Steutel
Publisher: CRC Press
ISBN: 020301412X
Category : Mathematics
Languages : en
Pages : 562
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Book Description
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.
Author: K. Balakrishnan
Publisher: Routledge
ISBN: 1351449125
Category : Mathematics
Languages : en
Pages : 664
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Book Description
The exponential distribution is one of the most significant and widely used distribution in statistical practice. It possesses several important statistical properties, and yet exhibits great mathematical tractability. This volume provides a systematic and comprehensive synthesis of the diverse literature on the theory and applications of the expon
Author: Marcelo G. Cruz
Publisher: John Wiley & Sons
ISBN: 1118118391
Category : Mathematics
Languages : en
Pages : 939
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Book Description
A one-stop guide for the theories, applications, and statistical methodologies essential to operational risk Providing a complete overview of operational risk modeling and relevant insurance analytics, Fundamental Aspects of Operational Risk and Insurance Analytics: A Handbook of Operational Risk offers a systematic approach that covers the wide range of topics in this area. Written by a team of leading experts in the field, the handbook presents detailed coverage of the theories, applications, and models inherent in any discussion of the fundamentals of operational risk, with a primary focus on Basel II/III regulation, modeling dependence, estimation of risk models, and modeling the data elements. Fundamental Aspects of Operational Risk and Insurance Analytics: A Handbook of Operational Risk begins with coverage on the four data elements used in operational risk framework as well as processing risk taxonomy. The book then goes further in-depth into the key topics in operational risk measurement and insurance, for example diverse methods to estimate frequency and severity models. Finally, the book ends with sections on specific topics, such as scenario analysis; multifactor modeling; and dependence modeling. A unique companion with Advances in Heavy Tailed Risk Modeling: A Handbook of Operational Risk, the handbook also features: Discussions on internal loss data and key risk indicators, which are both fundamental for developing a risk-sensitive framework Guidelines for how operational risk can be inserted into a firm’s strategic decisions A model for stress tests of operational risk under the United States Comprehensive Capital Analysis and Review (CCAR) program A valuable reference for financial engineers, quantitative analysts, risk managers, and large-scale consultancy groups advising banks on their internal systems, the handbook is also useful for academics teaching postgraduate courses on the methodology of operational risk.
Author: Samuel Kotz
Publisher: Springer Science & Business Media
ISBN: 146120173X
Category : Mathematics
Languages : en
Pages : 358
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Book Description
This book describes the inferential and modeling advantages that this distribution, together with its generalizations and modifications, offers. The exposition systematically unfolds with many examples, tables, illustrations, and exercises. A comprehensive index and extensive bibliography also make this book an ideal text for a senior undergraduate and graduate seminar on statistical distributions, or for a short half-term academic course in statistics, applied probability, and finance.
Author: Themistocles M. Rassias
Publisher: Springer
ISBN: 1493911066
Category : Mathematics
Languages : en
Pages : 783
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Book Description
The contributions in this volume have been written by eminent scientists from the international mathematical community and present significant advances in several theories, methods and problems of Mathematical Analysis, Discrete Mathematics, Geometry and their Applications. The chapters focus on both old and recent developments in Functional Analysis, Harmonic Analysis, Complex Analysis, Operator Theory, Combinatorics, Functional Equations, Differential Equations as well as a variety of Applications. The book also contains some review works, which could prove particularly useful for a broader audience of readers in Mathematical Sciences, and especially to graduate students looking for the latest information.
Author: A.M. Mathai
Publisher: Springer Science & Business Media
ISBN: 0387758941
Category : Science
Languages : en
Pages : 480
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Book Description
This book, written by a highly distinguished author, provides the required mathematical tools for researchers active in the physical sciences. The book presents a full suit of elementary functions for scholars at PhD level. The opening chapter introduces elementary classical special functions. The final chapter is devoted to the discussion of functions of matrix argument in the real case. The text and exercises have been class-tested over five different years.
Author: Ole E Barndorff-Nielsen
Publisher: Springer
ISBN: 3540323856
Category : Mathematics
Languages : en
Pages : 351
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Book Description
This is the second of two volumes containing the revised and completed notes of lectures given at the school "Quantum Independent Increment Processes: Structure and Applications to Physics". This school was held at the Alfried-Krupp-Wissenschaftskolleg in Greifswald in March, 2003, and supported by the Volkswagen Foundation. The school gave an introduction to current research on quantum independent increment processes aimed at graduate students and non-specialists working in classical and quantum probability, operator algebras, and mathematical physics. The present second volume contains the following lectures: "Random Walks on Finite Quantum Groups" by Uwe Franz and Rolf Gohm, "Quantum Markov Processes and Applications in Physics" by Burkhard Kümmerer, Classical and Free Infinite Divisibility and Lévy Processes" by Ole E. Barndorff-Nielsen, Steen Thorbjornsen, and "Lévy Processes on Quantum Groups and Dual Groups" by Uwe Franz.
