"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.

Probability is a vital measure in numerous disciplines, from bioinformatics and econometrics to finance/insurance and computer science. Developed from a successful course, "Fundamental Probability: A Computational Approach" provides an engaging and hands-on introduction to this important topic. Whilst the theory is explored in detail, this book also emphasises practical applications, with the presentation of a large variety of examples and exercises, along with generous use of computational tools.

Based on international teaching experience with students of statistics, mathematics, finance and econometrics, the book: Presents new, innovative material alongside the classic theory. Goes beyond standard presentations by carefully introducing and discussing more complex subject matter, including a richer use of combinatorics, runs and occupancy distributions, various multivariate sampling schemes, fat-tailed distributions, and several basic concepts used in finance. Emphasises computational matters and programming methods via generous use of examples in MATLAB. Includes a large, self-contained Calculus/Analysis appendix with derivations of all required tools, such as Leibniz' rule, exchange of derivative and integral, Fubini's theorem, and univariate and multivariate Taylor series. Presents over 150 end-of-chapter exercises, graded in terms of their difficulty, and accompanied by a full set of solutions online.

This book is intended as an introduction to the theory of probability for students in biology, mathematics, statistics, economics, engineering, finance, and computer science who possess the prerequisite knowledge of basic calculus and linear algebra.

Praxisorientiertes Fachbuch der Interferenzstatistik mit den neuesten Entwicklungen aus diesem standig wachsenden Wissensgebiet. Dieses ubersichtlich und zugangliche Fachbuch richtet sich an Studenten hoeherer Semester, prasentiert die Interferenzstatistik ausfuhrlich und praxisorientiert und stellt Ergebnisableitungen sowie MATLAB-Programme umfassend dar, erganzt um Erlauterungen. Besonderes Augenmerk liegt auf einzelnen bedeutenden Aspekten, auf einer intuitiven Herangehensweise und auf Diskussionen. Der Blick auf die Interferenzstatistik ist dabei uberaus modern. Inhalte neben den klassischen Themen rund um die mathematische Statistik: intuitive Prasentation von Einfach-/Doppel-Bootstraps bei der Berechnung von Konfidenzintervallen, Schrumpfungsschatzung, Schatzung des maximalen Moments sowie eine Vielzahl vom Methoden der Punktschatzung, maximale Wahrscheinlichkeit, Anwendung von charakteristischen Funktionen und indirekte Interferenz. Zu allen Methoden gibt es praktische Beispiele. Ausfuhrlich behandelt werden Schatzprobleme und deren Loesung in Verbindung mit der diskreten Mischung bei Normalverteilungen. Durchgangig liegt der Schwerpunkt auf nicht-Gaussschen Verteilungen, einschliesslich der ausfuhrlichen Behandlung der stabilen Pareto-Verteilung und der schnellen Berechnung von nicht-zentralen Student-t-Tests. Ein komplettes Kapitel widmet sich der Optimierung, darunter der Entwicklung von Hessian-Methoden, heuristische/genetische Algorithmen, die keine Kontinuitat erfordern. Die entsprechenden MATLAB-Codes werden zur Verfugung gestellt. Der Fokus liegt auch auf Berechnungen, die das Thema greifbar und fur die Studierenden zuganglich machen.