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1. |
Record Nr. |
UNINA9910813761303321 |
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Autore |
Ng Kai Wang |
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Titolo |
Dirichlet and related distributions : theory, methods and applications / / Kai Wang Ng, Guo-Liang Tian, Man-Lai Tang |
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Pubbl/distr/stampa |
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Hoboken, NJ, : Wiley, 2011 |
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ISBN |
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1-283-40560-1 |
9786613405609 |
1-119-99841-7 |
1-119-99586-8 |
1-119-99578-7 |
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Descrizione fisica |
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1 online resource (338 p.) |
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Collana |
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Wiley series in probability and statistics |
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Classificazione |
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Altri autori (Persone) |
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TianGuo-Liang |
TangMan-Lai |
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Disciplina |
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Soggetti |
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Distribution (Probability theory) |
Dirichlet problem |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Description based upon print version of record. |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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Dirichlet and Related Distributions: Theory, Methods and Applications; Contents; Preface; Acknowledgments; List of abbreviations; List of symbols; List of figures; List of tables; 1 Introduction; 1.1 Motivating examples; 1.2 Stochastic representation and the d= operator; 1.2.1 Definition of stochastic representation; 1.2.2 More properties on the d = operator; 1.3 Beta and inverted beta distributions; 1.4 Some useful identities and integral formulae; 1.4.1 Partial-fraction expansion; 1.4.2 Cambanis-Keener-Simons integral formulae; 1.4.3 Hermite-Genocchi integral formula |
1.5 The Newton-Raphson algorithm1.6 Likelihood in missing-data problems; 1.6.1 Missing-data mechanism; 1.6.2 The expectation-maximization (EM) algorithm; 1.6.3 The expectation/conditional maximization (ECM) algorithm; 1.6.4 The EM gradient algorithm; 1.7 Bayesian MDPs and inversion of Bayes' formula; 1.7.1 The data augmentation (DA) algorithm; 1.7.2 True nature of Bayesian MDP: inversion of Bayes' formula; 1.7.3 Explicit solution to the DA integral |
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equation; 1.7.4 Sampling issues in Bayesian MDPs; 1.8 Basic statistical distributions; 1.8.1 Discrete distributions |
1.8.2 Continuous distributions2 Dirichlet distribution; 2.1 Definition and basic properties; 2.1.1 Density function and moments; 2.1.2 Stochastic representations and mode; 2.2 Marginal and conditional distributions; 2.3 Survival function and cumulative distribution function; 2.3.1 Survival function; 2.3.2 Cumulative distribution function; 2.4 Characteristic functions; 2.4.1 The characteristic function of u ~ U(Tn); 2.4.2 The characteristic function of v ~ U(Tn); 2.4.3 The characteristic function of a Dirichlet random vector; 2.5 Distribution for linear function of a Dirichlet random vector |
2.5.1 Density for linear function of v ~ U(Vn)2.5.2 Density for linear function of u ~ U(Tn); 2.5.3 A unified approach to linear functions of variables and order statistics; 2.5.4 Cumulative distribution function for linear function of a Dirichlet random vector; 2.6 Characterizations; 2.6.1 Mosimann's characterization; 2.6.2 Darroch and Ratcliff's characterization; 2.6.3 Characterization through neutrality; 2.6.4 Characterization through complete neutrality; 2.6.5 Characterization through global and local parameter independence; 2.7 MLEs of the Dirichlet parameters |
2.7.1 MLE via the Newton-Raphson algorithm2.7.2 MLE via the EM gradient algorithm; 2.7.3 Analyzing serum-protein data of Pekin ducklings; 2.8 Generalized method of moments estimation; 2.8.1 Method of moments estimation; 2.8.2 Generalized method of moments estimation; 2.9 Estimation based on linear models; 2.9.1 Preliminaries; 2.9.2 Estimation based on individual linear models; 2.9.3 Estimation based on the overall linear model; 2.10 Application in estimating ROC area; 2.10.1 The ROC curve; 2.10.2 The ROC area; 2.10.3 Computing the posterior density of the ROC area |
2.10.4 Analyzing the mammogram data of breast cancer |
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Sommario/riassunto |
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The Dirichlet distribution appears in many areas of application, which include modelling of compositional data, Bayesian analysis, statistical genetics, and nonparametric inference. This book provides a comprehensive review of the Dirichlet distribution and two extended versions, the Grouped Dirichlet Distribution (GDD) and the Nested Dirichlet Distribution (NDD), arising from likelihood and Bayesian analysis of incomplete categorical data and survey data with non-response. The theoretical properties and applications are also reviewed in detail for other related distributions, such as the in |
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2. |
Record Nr. |
UNINA9910383828303321 |
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Autore |
Sibley Martin |
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Titolo |
Optical Communications : Components and Systems / / by Martin Sibley |
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Pubbl/distr/stampa |
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Cham : , : Springer International Publishing : , : Imprint : Springer, , 2020 |
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ISBN |
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Edizione |
[3rd ed. 2020.] |
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Descrizione fisica |
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1 online resource (XVII, 250 p. 98 illus.) |
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Disciplina |
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Soggetti |
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Microwaves |
Optical engineering |
Lasers |
Photonics |
Optical materials |
Electronics - Materials |
Electrical engineering |
Microwaves, RF and Optical Engineering |
Optics, Lasers, Photonics, Optical Devices |
Optical and Electronic Materials |
Communications Engineering, Networks |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Sommario/riassunto |
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The long-awaited third edition of this classic textbook provides a genuinely accessible introduction to the principles and technology of optical communication systems. It takes the reader from the fundamentals of light propagation in optical fibre, through materials and fabrication methods, light sources and modulation, to photodiodes and receiver design, and concludes with a chapter looking at system level integration. Updated throughout, major changes for this third edition include: - coverage of advanced semiconductor laser diode structures (VCSELs and DFBs) - an extended section on fibre amplifiers and lasers - updated discussion of avalanche photodiode structures - |
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expanded coverage of transimpedance and optical preamplifiers - new sections on free-space optical links, VLC, ethernet links, coherent detection and terabit systems Enhanced with worked examples and end-of-chapter problem sets, the book is aimed at advanced undergraduate and graduate students in electronic engineering, optical science and applied physics, and is ideally suited for adoption as a course text. |
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