LEADER 05553nam 2200697 a 450 001 9911018958403321 005 20200520144314.0 010 $a9786611002091 010 $a9781281002099 010 $a1281002097 010 $a9780470035061 010 $a0470035064 010 $a9780470035054 010 $a0470035056 035 $a(CKB)1000000000357149 035 $a(EBL)315055 035 $a(SSID)ssj0000180967 035 $a(PQKBManifestationID)11177736 035 $a(PQKBTitleCode)TC0000180967 035 $a(PQKBWorkID)10150935 035 $a(PQKB)11454891 035 $a(MiAaPQ)EBC315055 035 $a(PPN)170217272 035 $a(OCoLC)181368510 035 $a(FR-PaCSA)41000260 035 $a(FRCYB41000260)41000260 035 $a(Perlego)2770067 035 $a(EXLCZ)991000000000357149 100 $a20070511d2007 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aIntermediate probability $ea computational approach /$fMarc S. Paolella 210 $aChichester, England ;$aHoboken, NJ $cJohn Wiley$dc2007 215 $a1 online resource (431 p.) 300 $aDescription based upon print version of record. 311 08$a9780470026373 311 08$a0470026375 320 $aIncludes bibliographical references (p. [401]-411) and index. 327 $aIntermediate Probability; Chapter Listing; Contents; Preface; Part I Sums of Random Variables; 1 Generating functions; 1.1 The moment generating function; 1.1.1 Moments and the m.g.f.; 1.1.2 The cumulant generating function; 1.1.3 Uniqueness of the m.g.f.; 1.1.4 Vector m.g.f.; 1.2 Characteristic functions; 1.2.1 Complex numbers; 1.2.2 Laplace transforms; 1.2.3 Basic properties of characteristic functions; 1.2.4 Relation between the m.g.f. and c.f.; 1.2.5 Inversion formulae for mass and density functions; 1.2.6 Inversion formulae for the c.d.f.; 1.3 Use of the fast Fourier transform 327 $a1.3.1 Fourier series1.3.2 Discrete and fast Fourier transforms; 1.3.3 Applying the FFT to c.f. inversion; 1.4 Multivariate case; 1.5 Problems; 2 Sums and other functions of several random variables; 2.1 Weighted sums of independent random variables; 2.2 Exact integral expressions for functions of two continuous random variables; 2.3 Approximating the mean and variance; 2.4 Problems; 3 The multivariate normal distribution; 3.1 Vector expectation and variance; 3.2 Basic properties of the multivariate normal; 3.3 Density and moment generating function; 3.4 Simulation and c.d.f. calculation 327 $a3.5 Marginal and conditional normal distributions3.6 Partial correlation; 3.7 Joint distribution of X and S2 for i.i.d. normal samples; 3.8 Matrix algebra; 3.9 Problems; Part II Asymptotics and Other Approximations; 4 Convergence concepts; 4.1 Inequalities for random variables; 4.2 Convergence of sequences of sets; 4.3 Convergence of sequences of random variables; 4.3.1 Convergence in probability; 4.3.2 Almost sure convergence; 4.3.3 Convergence in r-mean; 4.3.4 Convergence in distribution; 4.4 The central limit theorem; 4.5 Problems; 5 Saddlepoint approximations; 5.1 Univariate 327 $a5.1.1 Density saddlepoint approximation5.1.2 Saddlepoint approximation to the c.d.f.; 5.1.3 Detailed illustration: the normal-Laplace sum; 5.2 Multivariate; 5.2.1 Conditional distributions; 5.2.2 Bivariate c.d.f. approximation; 5.2.3 Marginal distributions; 5.3 The hypergeometric functions 1F1 and 2F1; 5.4 Problems; 6 Order statistics; 6.1 Distribution theory for i.i.d. samples; 6.1.1 Univariate; 6.1.2 Multivariate; 6.1.3 Sample range and midrange; 6.2 Further examples; 6.3 Distribution theory for dependent samples; 6.4 Problems; Part III More Flexible and Advanced Random Variables 327 $a7 Generalizing and mixing7.1 Basic methods of extension; 7.1.1 Nesting and generalizing constants; 7.1.2 Asymmetric extensions; 7.1.3 Extension to the real line; 7.1.4 Transformations; 7.1.5 Invention of flexible forms; 7.2 Weighted sums of independent random variables; 7.3 Mixtures; 7.3.1 Countable mixtures; 7.3.2 Continuous mixtures; 7.4 Problems; 8 The stable Paretian distribution; 8.1 Symmetric stable; 8.2 Asymmetric stable; 8.3 Moments; 8.3.1 Mean; 8.3.2 Fractional absolute moment proof I; 8.3.3 Fractional absolute moment proof II; 8.4 Simulation; 8.5 Generalized central limit theorem 327 $a9 Generalized inverse Gaussianand generalized hyperbolic distributions 330 $aIntermediate 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 theor 606 $aDistribution (Probability theory)$xMathematical models 606 $aProbabilities 615 0$aDistribution (Probability theory)$xMathematical models. 615 0$aProbabilities. 676 $a519.2 700 $aPaolella$b Marc S$0614467 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9911018958403321 996 $aIntermediate probability$94422163 997 $aUNINA