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Fundamental probability : a computational approach
| Fundamental probability : a computational approach |
| Autore | Paolella Marc S |
| Pubbl/distr/stampa | [Place of publication not identified], : John Wiley, 2006 |
| Disciplina | 519.2 |
| Soggetto topico |
Probabilities - Data processing
Mathematical Statistics Mathematics Physical Sciences & Mathematics |
| ISBN | 0-470-03535-8 |
| Classificazione | 31.70 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Combinatorics -- Probability spaces and counting -- Symmetric spaces and conditioning -- Univariate random variables -- Multivariate random variables -- Sums of random variables -- Continuous univariate random variables -- Joint and conditional random variables -- Multivariate transformations. |
| Record Nr. | UNINA-9910144722803321 |
Paolella Marc S
|
||
| [Place of publication not identified], : John Wiley, 2006 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Fundamental probability : a computational approach
| Fundamental probability : a computational approach |
| Autore | Paolella Marc S |
| Pubbl/distr/stampa | [Place of publication not identified], : John Wiley, 2006 |
| Disciplina | 519.2 |
| Soggetto topico |
Probabilities - Data processing
Mathematical Statistics Mathematics Physical Sciences & Mathematics |
| ISBN | 0-470-03535-8 |
| Classificazione | 31.70 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Combinatorics -- Probability spaces and counting -- Symmetric spaces and conditioning -- Univariate random variables -- Multivariate random variables -- Sums of random variables -- Continuous univariate random variables -- Joint and conditional random variables -- Multivariate transformations. |
| Record Nr. | UNINA-9910830300903321 |
|
Paolella Marc S
|
||
| [Place of publication not identified], : John Wiley, 2006 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Fundamental probability : a computational approach
| Fundamental probability : a computational approach |
| Autore | Paolella Marc S |
| Pubbl/distr/stampa | [Place of publication not identified], : John Wiley, 2006 |
| Disciplina | 519.2 |
| Soggetto topico |
Probabilities - Data processing
Mathematical Statistics Mathematics Physical Sciences & Mathematics |
| ISBN | 0-470-03535-8 |
| Classificazione | 31.70 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Combinatorics -- Probability spaces and counting -- Symmetric spaces and conditioning -- Univariate random variables -- Multivariate random variables -- Sums of random variables -- Continuous univariate random variables -- Joint and conditional random variables -- Multivariate transformations. |
| Record Nr. | UNINA-9911019187103321 |
|
Paolella Marc S
|
||
| [Place of publication not identified], : John Wiley, 2006 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Intermediate probability [[electronic resource] ] : a computational approach / / Marc S. Paolella
| Intermediate probability [[electronic resource] ] : a computational approach / / Marc S. Paolella |
| Autore | Paolella Marc S |
| Pubbl/distr/stampa | Chichester, England ; ; Hoboken, NJ, : John Wiley, c2007 |
| Descrizione fisica | 1 online resource (431 p.) |
| Disciplina | 519.2 |
| Soggetto topico |
Distribution (Probability theory) - Mathematical models
Probabilities |
| ISBN |
1-281-00209-7
9786611002091 0-470-03506-4 0-470-03505-6 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intermediate 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
1.3.1 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 3.5 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 5.1.1 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 7 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 9 Generalized inverse Gaussianand generalized hyperbolic distributions |
| Record Nr. | UNINA-9910143585303321 |
|
Paolella Marc S
|
||
| Chichester, England ; ; Hoboken, NJ, : John Wiley, c2007 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Intermediate probability [[electronic resource] ] : a computational approach / / Marc S. Paolella
| Intermediate probability [[electronic resource] ] : a computational approach / / Marc S. Paolella |
| Autore | Paolella Marc S |
| Pubbl/distr/stampa | Chichester, England ; ; Hoboken, NJ, : John Wiley, c2007 |
| Descrizione fisica | 1 online resource (431 p.) |
| Disciplina | 519.2 |
| Soggetto topico |
Distribution (Probability theory) - Mathematical models
Probabilities |
| ISBN |
1-281-00209-7
9786611002091 0-470-03506-4 0-470-03505-6 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intermediate 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
1.3.1 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 3.5 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 5.1.1 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 7 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 9 Generalized inverse Gaussianand generalized hyperbolic distributions |
| Record Nr. | UNINA-9910829851403321 |
|
Paolella Marc S
|
||
| Chichester, England ; ; Hoboken, NJ, : John Wiley, c2007 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Intermediate probability : a computational approach / / Marc S. Paolella
| Intermediate probability : a computational approach / / Marc S. Paolella |
| Autore | Paolella Marc S |
| Pubbl/distr/stampa | Chichester, England ; ; Hoboken, NJ, : John Wiley, c2007 |
| Descrizione fisica | 1 online resource (431 p.) |
| Disciplina | 519.2 |
| Soggetto topico |
Distribution (Probability theory) - Mathematical models
Probabilities |
| ISBN |
9786611002091
9781281002099 1281002097 9780470035061 0470035064 9780470035054 0470035056 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intermediate 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
1.3.1 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 3.5 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 5.1.1 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 7 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 9 Generalized inverse Gaussianand generalized hyperbolic distributions |
| Record Nr. | UNINA-9911018958403321 |
|
Paolella Marc S
|
||
| Chichester, England ; ; Hoboken, NJ, : John Wiley, c2007 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||