Intermediate Probability

Beschreibung

Intermediate Probability is the natural extension of the author'sFundamental Probability. It details several highly importanttopics, from standard ones such as order statistics, multivariatenormal, and convergence concepts, to more advanced ones which areusually not addressed at this mathematical level, or have neverpreviously appeared in textbook form. The author adopts acomputational approach throughout, allowing the reader to directlyimplement the methods, thus greatly enhancing the learningexperience and clearly illustrating the applicability, strengths,and weaknesses of the theory. The book: * Places great emphasis on the numeric computation ofconvolutions of random variables, via numeric integration,inversion theorems, fast Fourier transforms, saddlepointapproximations, and simulation. * Provides introductory material to required mathematical topicssuch as complex numbers, Laplace and Fourier transforms, matrixalgebra, confluent hypergeometric functions, digamma functions, andBessel functions. * Presents full derivation and numerous computational methods ofthe stable Paretian and the singly and doubly non-centraldistributions. * A whole chapter is dedicated to mean-variance mixtures, NIG,GIG, generalized hyperbolic and numerous relateddistributions. * A whole chapter is dedicated to nesting, generalizing, andasymmetric extensions of popular distributions, as have becomepopular 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 meansthat self-study is easily possible, making the book ideal forsenior undergraduate and graduate students of mathematics,statistics, econometrics, finance, insurance, and computer science,as well as researchers and professional statisticians working inthese fields.

Autor*in

Marc Paolella

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Angewandte Wahrscheinlichkeitsrechnung u. Statistik Applied Probability & Statistics Probability & Mathematical Statistics Statistics Statistik Wahrscheinlichkeitsrechnung u. mathematische Statistik

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"I thoroughly enjoyed Intermediate Probability. I was sothrilled with it that I have shared it with some of my colleagues.They have called it a 'gold mine' of problems and resources, anddescribing it as 'amazing.' ... I highly recommend it."(Journal of the American Statistical Association, September2009) "The reader-friendly style of the text itself would make thebook appropriate for self-study or classroom adoption." (MAAReviews, December 2007)
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