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Intermediate Probability: A Computational Approach
John Wiley and Sons Ltd, Aug 2007, Pages: 488
Many of the traditional and older advanced texts do not cover the newer topics in probability such as Paretian distribution and noncentral distributions and saddlepoint approximation. The material is only covered in research monographs or in journal articles. This text introduces these topics in the context of real-life examples and making full use of the available computer software.
The contents include a highly accessible introduction to inversion theorems and their numerical implementation, convolution of random variables, distribution approximations, and the method of saddlepoint approximation (SPA); plus an overview of order statistics (with an introduction to extreme value theory) and the multivariate normal distribution, respectively. Other advanced topics cover the ideas of nesting, generalizing, asymmetric extensions and mixtures; the stable Paretian distribution, with emphasis on its computation, basic properties, and uses; the (generalized) inverse Gaussian and (generalized) hyperbolic distributions, and their connections; and noncentral distributions and quadratic forms.
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 the author:
Marc S Paolella, Swiss Banking Institute, University of Zurich, Switzerland. Associate Professor. Previous career includes: Director of the Institute of Statistics and Econometrics, Kiel University; Statistical Consultant, Colorado State University; Statistical Programmer at Health Economics Research Inc. Waltham. MA USA. Refereed papers in Journal of the American Statistical Association, Journal of Forecasting, Bernoulli, Statistics and Computing, Applied Economics Quarterly.
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