{"product_id":"intermediate-probability-9780470026373","title":"Intermediate Probability","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eIntermediate 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.  \u003cp\u003eThe book:\u003c\/p\u003e \u003cul\u003e \u003cli\u003ePlaces great emphasis on the numeric computation of convolutions of random variables, via numeric integration, inversion theorems, fast Fourier transforms, saddlepoint approximations, and simulation.\u003c\/li\u003e \u003cli\u003eProvides introductory material to required mathematical topics such as complex numbers, Laplace and Fourier transforms, matrix algebra, confluent hypergeometric\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"I thoroughly enjoyed \u003ci\u003eIntermediate Probability\u003c\/i\u003e. I was so thrilled with it that I have shared it with some of my colleagues. They have called it a 'gold mine' of problems and resources, and describing it as 'amazing.' ... I highly recommend it.\" (\u003ci\u003eJournal of the American Statistical Association\u003c\/i\u003e, September 2009)\u003cbr\u003e \u003cbr\u003e   \u003cp\u003e\"The reader-friendly style of the text itself would make the book appropriate for self-study or classroom adoption.\" (\u003ci\u003eMAA Reviews\u003c\/i\u003e, December 2007)\u003c\/p\u003e\n\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface.  \u003cp\u003e\u003cb\u003eI Sums of Random Variables.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Generating functions.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 The moment generating function.\u003c\/p\u003e \u003cp\u003e1.2 Characteristic functions.\u003c\/p\u003e \u003cp\u003e1.3 Use of the fast Fourier transform.\u003c\/p\u003e \u003cp\u003e1.4 Multivariate case.\u003c\/p\u003e \u003cp\u003e1.5 Problems.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Sums and other functions of several random variables.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Weighted sums of independent random variables.\u003c\/p\u003e \u003cp\u003e2.2 Exact integral expressions for functions of two continuous random\u003c\/p\u003e \u003cp\u003evariables.\u003c\/p\u003e \u003cp\u003e2.3 Approximating the mean and variance.\u003c\/p\u003e \u003cp\u003e2.4 Problems.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 The multivariate normal distribution.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Vector expectation and variance.\u003c\/p\u003e \u003cp\u003e3.2 Basic properties of the multivariate normal.\u003c\/p\u003e \u003cp\u003e3.3 Density and moment generating function.\u003c\/p\u003e \u003cp\u003e3.4 Simulation and c.d.f. calculation.\u003c\/p\u003e \u003cp\u003e3.5 Marginal and conditional normal distributions.\u003c\/p\u003e \u003cp\u003e3.6 Partial correlation.\u003c\/p\u003e \u003cp\u003e3.7 Joint distribution of Xbar and S2 for i.i.d. normal samples.\u003c\/p\u003e \u003cp\u003e3.8 Matrix algebra.\u003c\/p\u003e \u003cp\u003e3.9 Problems.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eII Asymptotics and Other Approximations.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Convergence concepts.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Inequalities for random variables.\u003c\/p\u003e \u003cp\u003e4.2 Convergence of sequences of sets.\u003c\/p\u003e \u003cp\u003e4.3 Convergence of sequences of random variables.\u003c\/p\u003e \u003cp\u003e4.4 The central limit theorem.\u003c\/p\u003e \u003cp\u003e4.5 Problems.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Saddlepoint approximations.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Univariate.\u003c\/p\u003e \u003cp\u003e5.2 Multivariate.\u003c\/p\u003e \u003cp\u003e5.3 The hypergeometric functions 1F1 and 2F1.\u003c\/p\u003e \u003cp\u003e5.4 Problems.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Order statistics.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Distribution theory for i.i.d. samples.\u003c\/p\u003e \u003cp\u003e6.2 Further examples.\u003c\/p\u003e \u003cp\u003e6.3 Distribution theory for dependent samples.\u003c\/p\u003e \u003cp\u003e6.4 Problems.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eIII More Flexible and Advanced Random Variables.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Generalizing and mixing.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Basic methods of extension.\u003c\/p\u003e \u003cp\u003e7.2 Weighted sums of independent random variables.\u003c\/p\u003e \u003cp\u003e7.3 Mixtures.\u003c\/p\u003e \u003cp\u003e7.4 Problems.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 The stable Paretian distribution.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Symmetric stable.\u003c\/p\u003e \u003cp\u003e8.2 Asymmetric stable.\u003c\/p\u003e \u003cp\u003e8.3 Moments.\u003c\/p\u003e \u003cp\u003e8.4 Simulation.\u003c\/p\u003e \u003cp\u003e8.5 Generalized central limit theorem.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Generalized inverse Gaussian and generalized hyperbolic distributions.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Introduction.\u003c\/p\u003e \u003cp\u003e9.2 The modified Bessel function of the third kind.\u003c\/p\u003e \u003cp\u003e9.3 Mixtures of normal distributions.\u003c\/p\u003e \u003cp\u003e9.4 The generalized inverse Gaussian distribution.\u003c\/p\u003e \u003cp\u003e9.5 The generalized hyperbolic distribution.\u003c\/p\u003e \u003cp\u003e9.6 Properties of the GHyp distribution family.\u003c\/p\u003e \u003cp\u003e9.7 Problems.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Noncentral distributions.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Noncentral chi-square.\u003c\/p\u003e \u003cp\u003e10.2 Singly and doubly noncentral F.\u003c\/p\u003e \u003cp\u003e10.3 Noncentral beta.\u003c\/p\u003e \u003cp\u003e10.4 Singly and doubly noncentral t.\u003c\/p\u003e \u003cp\u003e10.5 Saddlepoint uniqueness for the doubly noncentral F.\u003c\/p\u003e \u003cp\u003e10.6 Problems.\u003c\/p\u003e \u003cp\u003eA Notation and distribution tables.\u003c\/p\u003e \u003cp\u003eReferences.\u003c\/p\u003e \u003cp\u003eIndex.\u003c\/p\u003e\n\u003c\/li\u003e\n\u003c\/ul\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49402262749527,"sku":"9780470026373","price":114.26,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780470026373.jpg?v=1730479873","url":"https:\/\/bookcurl.com\/products\/intermediate-probability-9780470026373","provider":"Book Curl","version":"1.0","type":"link"}