Intermediate Probability (PDF)

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.