Intermediate Probability: a Computational Approach is Ideal for Students of Mathematics, Statistics, Econometrics, Finance, Insurance, and Computer Science, as Well as Researchers and Professional Statisticians Working in These Fields.DUBLIN, Ireland -- Research and Markets (http://www.researchandmarkets.com/reports/c70875) has announced the addition of "Intermediate Probability: A Computational Approach" to their offering.
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 convolution /con·vo·lu·tion/ (-loo´shun) a tortuous irregularity or elevation caused by the infolding of a structure upon itself. 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
In probability theory and statistics, a multivariate normal distribution, also sometimes called a multivariate Gaussian 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.
* Places great emphasis on the numeric computation of convolutions of random variables, via numeric integration, inversion theorems, fast Fourier transforms See FFT.
(algorithm) Fast Fourier Transform - (FFT) An algorithm for computing the Fourier transform of a set of discrete data values. Given a finite set of data points, for example a periodic sampling taken from a real-world signal, the FFT expresses the data in terms of , saddlepoint approximations, and simulation.
* Provides introductory material to required mathematical topics such as complex numbers, Laplace and Fourier transforms, matrix algebra Noun 1. matrix algebra - the part of algebra that deals with the theory of matrices
diagonalisation, diagonalization - changing a square matrix to diagonal form (with all non-zero elements on the principal diagonal); "the diagonalization of a normal matrix by a , 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 NIG National Institute of Genetics
NIG National Insurance Guarantee Corporation Ltd. (UK insurance company)
NIG Navy Inspector General
NIG New in Germany
NIG not in goal (soccer) , GIG, generalized hyperbolic hy·per·bol·ic also hy·per·bol·i·cal
1. Of, relating to, or employing hyperbole.
a. Of, relating to, or having the form of a hyperbola.
b. 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 Statisticians or people who made notable contributions to the theories of statistics, or related aspects of probability, or machine learning: A to E
About the author:
Marc S Paolella, Swiss Banking Institute, University of Zurich History
The University of Zurich was founded in 1833 with existing colleges of theology (founded by Huldrych Zwingli in 1525), law and medicine merged together with a new faculty of Philosophy. , Switzerland. Associate Professor. Previous career includes: Director of the Institute of Statistics and Econometrics, Kiel University; Statistical Consultant, Colorado State University Colorado State University, at Fort Collins; land-grant with state and federal support; chartered 1870, opened 1879 as an agricultural college, assumed present name in 1957. There is a veterinary teaching hospital, an agricultural campus, and a research campus. ; Statistical Programmer at Health Economics Research Inc. Waltham. MA USA. Refereed papers in Journal of the American Statistical Association Established in 1888 and published quarterly in March, June, September, and December, the Journal of the American Statistical Association (JASA) has long been considered the premier journal of statistical science. , Journal of Forecasting, Bernoulli, Statistics and Computing, Applied Economics Quarterly.
* Sums of Random Variables
* Sums and other functions of several random variables
* The multivariate normal distribution
* Convergence concepts
* Saddlepoint approximations
* Order statistics
* Generalizing and mixing
* The stable Paretian distribution
* Generalized inverse In mathematics, a generalized inverse or pseudoinverse of a matrix A is a matrix that has some properties of the inverse matrix of A but not necessarily all of them. The term "the pseudoinverse" commonly means the Moore-Penrose pseudoinverse. Gaussian and generalized hyperbolic distributions.
* Noncentral distributions
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