Intermediate Probability: A Computational Approach - Hardcover

Paolella, Marc S.

Hardcover

ISBN 10: 0470026375 ISBN 13: 9780470026373

Publisher: Wiley-Interscience, 2007

Synopsis

Intermediate Probability is the natural extension of the author's Fundamental Probability. It details several highly important topics, from standard ones such as order statistics, multivariate normal, and convergence concepts, to more advanced ones which are usually not addressed at this mathematical level, or have never previously appeared in textbook form. The author adopts a computational approach throughout, allowing the reader to directly implement the methods, thus greatly enhancing the learning experience and clearly illustrating the applicability, strengths, and weaknesses of the theory.

The book:

• Places great emphasis on the numeric computation of convolutions of random variables, via numeric integration, inversion theorems, fast Fourier transforms, saddlepoint approximations, and simulation.
• Provides introductory material to required mathematical topics such as complex numbers, Laplace and Fourier transforms, matrix algebra, confluent hypergeometric functions, digamma functions, and Bessel functions.
• Presents full derivation and numerous computational methods of the stable Paretian and the singly and doubly non-central distributions.
• A whole chapter is dedicated to mean-variance mixtures, NIG, GIG, generalized hyperbolic and numerous related distributions.
• A whole chapter is dedicated to nesting, generalizing, and asymmetric extensions of popular distributions, as have become popular in empirical finance and other applications.
• Provides all essential programming code in Matlab and R.

The user-friendly style of writing and attention to detail means that self-study is easily possible, making the book ideal for senior undergraduate and graduate students of mathematics, statistics, econometrics, finance, insurance, and computer science, as well as researchers and professional statisticians working in these fields.

About this title

About the Author

Marc S Paolella, Professor of Empirical Finance, Swiss Banking Institute, University of Zurich, Switzerland.

From the Back Cover

Intermediate Probability is the natural extension of the author's previous title, Fundamental Probability. It details all the essential topics, ranging from standard issues such as order statistics, multivariate normal, and convergence concepts, to more advanced subjects which are usually not addressed at this mathematical level, or have never previously appeared in textbook form. The author adopts a computational approach throughout, allowing the reader to directly implement the methods, thus greatly enhancing the learning experience and clearly illustrating the applicability, strengths, and weaknesses of the theory.

The book:

• Places great emphasis on the numeric computation of convolutions of random variables, via numeric integration, inversion theorems, fast Fourier transforms, saddlepoint approximations, and simulation.
• Provides introductory material to required mathematical topics such as complex numbers, Laplace and Fourier transforms, matrix algebra, confluent hypergeometric functions, digamma functions, and Bessel functions.
• Presents full derivation and numerous computational methods of the stable Paretian and the singly and doubly non-central distributions.
• Devotes a whole chapter to mean-variance mixtures, NIG, GIG, generalized hyperbolic and numerous related distributions.
• Features a chapter dedicated to nesting, generalizing, and asymmetric extensions of popular distributions, as have become popular in empirical finance and other applications.
• Provides all essential programming code in Matlab and R.

The user-friendly style of writing and attention to detail means that self-study is easily possible, making the book ideal for senior undergraduate and graduate students of mathematics, statistics, econometrics, finance, insurance, and computer science, as well as researchers and professional statisticians working in these fields.

The book:

• Places great emphasis on the numeric computation of convolutions of random variables, via numeric integration, inversion theorems, fast Fourier transforms, saddlepoint approximations, and simulation.
• Provides introductory material to required mathematical topics such as complex numbers, Laplace and Fourier transforms, matrix algebra, confluent hypergeometric functions, digamma functions, and Bessel functions.
• Presents full derivation and numerous computational methods of the stable Paretian and the singly and doubly non-central distributions.
• Devotes a whole chapter to mean-variance mixtures, NIG, GIG, generalized hyperbolic and numerous related distributions.
• Features a chapter dedicated to nesting, generalizing, and asymmetric extensions of popular distributions, as have become popular in empirical finance and other applications.
• Provides all essential programming code in Matlab and R.

The user-friendly style of writing and attention to detail means that self-study is easily possible, making the book ideal for senior undergraduate and graduate students of mathematics, statistics, econometrics, finance, insurance, and computer science, as well as researchers and professional statisticians working in these fields.

Edition details

• Publisher: Wiley-Interscience
• Publication date: 2007
• Language: English
• ISBN 10: 0470026375
• ISBN 13: 9780470026373
• Binding: Hardcover
• Edition number: 1
• Number of pages: 432