Intermediate Probability: A Computational Approach (Hardcover)

Description

"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.It 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. It 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. This book 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.  

Table of Contents

Pt. I  Sums of random variables  1
1  Generating functions  3
2  Sums and other functions of several random variables  65
3  The multivariate normal distribution  97
Pt. II  Asymptotics and other approximations  127
4  Convergence concepts  129
5  Saddlepoint approximations  169
6  Order statistics  203
Pt. III  More flexible and advanced random variables  237
7  Generalizing and mixing  239
8  The stable Paretian distribution  277
9  Generalized inverse Gaussian and generalized hyperbolic distributions  299
10  Noncentral distributions  341
A  Notation and distribution tables  389