"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 graduatestudents of mathematics,
statistics, econometrics, finance, insurance, and computer science,
as well as researchers and professional statisticians working in
these fields.
General
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