Info
- Utilizzare la checkbox di selezione a fianco di ciascun documento per attivare le funzionalità di stampa, invio email, download nei formati disponibili del (i) record.
Asymptotic expansions for infinite weighted convolutions of heavy tail distributions and application / / Ph. Barbe, W.P. McCormick
| Asymptotic expansions for infinite weighted convolutions of heavy tail distributions and application / / Ph. Barbe, W.P. McCormick |
| Autore | Barbe Philippe |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2009 |
| Descrizione fisica | 1 online resource (133 p.) |
| Disciplina | 519.2/4 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Distribution (Probability theory) - Mathematical models
Asymptotic expansions Stochastic processes |
| Soggetto genere / forma | Electronic books. |
| ISBN | 1-4704-0528-8 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""1. Introduction""; ""1.1. Prolegomenom""; ""1.2. Mathematical overview and heuristics""; ""2. Main result""; ""2.1. Some notation""; ""2.2. Asymptotic scales""; ""2.3. The Laplace characters""; ""2.4. Smoothly varying functions of finite order""; ""2.5. Asymptotic expansion for in finite weighted convolution""; ""3. Implementing the expansion""; ""3.1. How many terms are in the expansion?""; ""3.2. [sub(*)]-Asymptotic scales and functions of class m""; ""3.3. Tail calculus: From Laplace characters to linear algebra""; ""3.4. Some examples""
""3.5. Two terms expansion and second order regular variation""""3.6. Some open questions""; ""4. Applications""; ""4.1. ARMA models""; ""4.2. Tail index estimation""; ""4.3. Randomly weighted sums""; ""4.4. Compound sums""; ""4.5. Queueing theory""; ""4.6. Branching processes""; ""4.7. Infinitely divisible distributions""; ""4.8. Implicit transient renewal equation and iterative systems""; ""5. Preparing the proof""; ""5.1. Properties of Laplace characters""; ""5.2. Properties of smoothly varying functions of finite order""; ""6. Proof in the positive case"" ""6.1. Decomposition of the convolution into integral and multiplication operators""""6.2. Organizing the proof""; ""6.3. Regular variation and basic tail estimates""; ""6.4. The fundamental estimate""; ""6.5. Basic lemmas""; ""6.6. Inductions""; ""6.7. Conclusion""; ""7. Removing the sign restriction on the random variables""; ""7.1. Elementary properties of U[sub(H)]""; ""7.2. Basic expansion of U[sub(H)]""; ""7.3. A technical lemma""; ""7.4. Conditional expansion and removing conditioning""; ""8. Removing the sign restriction on the constants"" ""8.1. Neglecting terms involving the multiplication operators""""8.2. Substituting H[sup((k))] and G[sup((k))] by their expansions""; ""9. Removing the smoothness restriction""; ""Appendix. Maple code""; ""Bibliography"" |
| Record Nr. | UNINA-9910480112803321 |
Barbe Philippe
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 2009 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Asymptotic expansions for infinite weighted convolutions of heavy tail distributions and application / / Ph. Barbe, W.P. McCormick
| Asymptotic expansions for infinite weighted convolutions of heavy tail distributions and application / / Ph. Barbe, W.P. McCormick |
| Autore | Barbe Philippe |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2009 |
| Descrizione fisica | 1 online resource (133 p.) |
| Disciplina | 519.2/4 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Distribution (Probability theory) - Mathematical models
Asymptotic expansions Stochastic processes |
| ISBN | 1-4704-0528-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""1. Introduction""; ""1.1. Prolegomenom""; ""1.2. Mathematical overview and heuristics""; ""2. Main result""; ""2.1. Some notation""; ""2.2. Asymptotic scales""; ""2.3. The Laplace characters""; ""2.4. Smoothly varying functions of finite order""; ""2.5. Asymptotic expansion for in finite weighted convolution""; ""3. Implementing the expansion""; ""3.1. How many terms are in the expansion?""; ""3.2. [sub(*)]-Asymptotic scales and functions of class m""; ""3.3. Tail calculus: From Laplace characters to linear algebra""; ""3.4. Some examples""
""3.5. Two terms expansion and second order regular variation""""3.6. Some open questions""; ""4. Applications""; ""4.1. ARMA models""; ""4.2. Tail index estimation""; ""4.3. Randomly weighted sums""; ""4.4. Compound sums""; ""4.5. Queueing theory""; ""4.6. Branching processes""; ""4.7. Infinitely divisible distributions""; ""4.8. Implicit transient renewal equation and iterative systems""; ""5. Preparing the proof""; ""5.1. Properties of Laplace characters""; ""5.2. Properties of smoothly varying functions of finite order""; ""6. Proof in the positive case"" ""6.1. Decomposition of the convolution into integral and multiplication operators""""6.2. Organizing the proof""; ""6.3. Regular variation and basic tail estimates""; ""6.4. The fundamental estimate""; ""6.5. Basic lemmas""; ""6.6. Inductions""; ""6.7. Conclusion""; ""7. Removing the sign restriction on the random variables""; ""7.1. Elementary properties of U[sub(H)]""; ""7.2. Basic expansion of U[sub(H)]""; ""7.3. A technical lemma""; ""7.4. Conditional expansion and removing conditioning""; ""8. Removing the sign restriction on the constants"" ""8.1. Neglecting terms involving the multiplication operators""""8.2. Substituting H[sup((k))] and G[sup((k))] by their expansions""; ""9. Removing the smoothness restriction""; ""Appendix. Maple code""; ""Bibliography"" |
| Record Nr. | UNINA-9910788853703321 |
|
Barbe Philippe
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 2009 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Asymptotic expansions for infinite weighted convolutions of heavy tail distributions and application / / Ph. Barbe, W.P. McCormick
| Asymptotic expansions for infinite weighted convolutions of heavy tail distributions and application / / Ph. Barbe, W.P. McCormick |
| Autore | Barbe Philippe |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2009 |
| Descrizione fisica | 1 online resource (133 p.) |
| Disciplina | 519.2/4 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Distribution (Probability theory) - Mathematical models
Asymptotic expansions Stochastic processes |
| ISBN | 1-4704-0528-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""1. Introduction""; ""1.1. Prolegomenom""; ""1.2. Mathematical overview and heuristics""; ""2. Main result""; ""2.1. Some notation""; ""2.2. Asymptotic scales""; ""2.3. The Laplace characters""; ""2.4. Smoothly varying functions of finite order""; ""2.5. Asymptotic expansion for in finite weighted convolution""; ""3. Implementing the expansion""; ""3.1. How many terms are in the expansion?""; ""3.2. [sub(*)]-Asymptotic scales and functions of class m""; ""3.3. Tail calculus: From Laplace characters to linear algebra""; ""3.4. Some examples""
""3.5. Two terms expansion and second order regular variation""""3.6. Some open questions""; ""4. Applications""; ""4.1. ARMA models""; ""4.2. Tail index estimation""; ""4.3. Randomly weighted sums""; ""4.4. Compound sums""; ""4.5. Queueing theory""; ""4.6. Branching processes""; ""4.7. Infinitely divisible distributions""; ""4.8. Implicit transient renewal equation and iterative systems""; ""5. Preparing the proof""; ""5.1. Properties of Laplace characters""; ""5.2. Properties of smoothly varying functions of finite order""; ""6. Proof in the positive case"" ""6.1. Decomposition of the convolution into integral and multiplication operators""""6.2. Organizing the proof""; ""6.3. Regular variation and basic tail estimates""; ""6.4. The fundamental estimate""; ""6.5. Basic lemmas""; ""6.6. Inductions""; ""6.7. Conclusion""; ""7. Removing the sign restriction on the random variables""; ""7.1. Elementary properties of U[sub(H)]""; ""7.2. Basic expansion of U[sub(H)]""; ""7.3. A technical lemma""; ""7.4. Conditional expansion and removing conditioning""; ""8. Removing the sign restriction on the constants"" ""8.1. Neglecting terms involving the multiplication operators""""8.2. Substituting H[sup((k))] and G[sup((k))] by their expansions""; ""9. Removing the smoothness restriction""; ""Appendix. Maple code""; ""Bibliography"" |
| Record Nr. | UNINA-9910817264803321 |
|
Barbe Philippe
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 2009 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Combinatorial methods in discrete distributions [[electronic resource] /] / Charalambos A. Charalambides
| Combinatorial methods in discrete distributions [[electronic resource] /] / Charalambos A. Charalambides |
| Autore | Charalambides Ch. A |
| Pubbl/distr/stampa | Hoboken, N.J., : Wiley-Interscience, c2005 |
| Descrizione fisica | 1 online resource (440 p.) |
| Disciplina |
511.6
519.2/4 519.24 |
| Collana | Wiley series in probability and statistics |
| Soggetto topico |
Combinatorial analysis
Distribution (Probability theory) |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-280-27703-3
9786610277032 0-470-32376-0 0-471-73318-0 0-471-73317-2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
COMBINATORIAL METHODS IN DISCRETE DISTRIBUTIONS; Contents; Preface; 1 BASIC COMBINATORICS AND PROBABILITY; 1.1 Basic counting principles; 1.2 Recurrence relations; 1.3 Finite differences; 1.4 Discrete probability; 1.5 Inclusion and exclusion principle; 1.6 Distributions and moments of random variables; 1.7 Generating functions; 1.8 Reference notes; 1.9 Exercises and complements; 2 STIRLING NUMBERS; 2.1 Introduction; 2.2 Definitions and generating functions; 2.3 Explicit expressions and recurrence relations; 2.4 Generalized factorial coefficients
2.5 Enumeration of partitions by subsets and permutations by cycles2.6 Reference notes; 2.7 Exercises and complements; 3 GENERALIZED STIRLING AND LAH NUMBERS; 3.1 Introduction; 3.2 Associated Stirling numbers; 3.3 Associated generalized factorial coefficients; 3.4 Universal generating functions; 3.5 Generalized Stirling numbers; 3.6 Generalized Lah numbers; 3.7 Reference notes; 3.8 Exercises and complements; 4 OCCUPANCY DISTRIBUTIONS; 4.1 Introduction; 4.2 A random occupancy model; 4.3 Occupancy distributions; 4.4 Particular occupancy distributions; 4.4.1 Classical occupancy distribution 4.4.2 Restricted occupancy distribution4.4.3 Pseudo-contagious occupancy distribution; 4.4.4 Restricted Bose-Einstein occupancy distribution; 4.5 Statistical applications; 4.6 A general random occupancy model; 4.7 Reference notes; 4.8 Exercises and complements; 5 SEQUENTIAL OCCUPANCY DISTRIBUTIONS; 5.1 Introduction; 5.2 A sequential random occupancy model; 5.3 Sequential occupancy distributions; 5.4 Particular sequential occupancy distributions; 5.4.1 Sequential classical occupancy distributions; 5.4.2 Sequential restricted occupancy distributions 5.4.3 Sequential pseudo-contagious occupancy distributions5.5 Statistical applications; 5.6 A reduced sequential occupancy model; 5.7 Reference notes; 5.8 Exercises and complements; 6 CONVOLUTIONS OF TRUNCATED DISTRIBUTIONS; 6.1 Introduction; 6.2 Zero truncated discrete distributions; 6.3 Some particular convolutions; 6.3.1 Zero truncated Poisson distribution; 6.3.2 Logarithmic distribution; 6.3.3 Zero truncated binomial distribution; 6.3.4 Zero truncated negative binomial distribution; 6.4 General truncated discrete distributions; 6.5 Statistical applications 6.5.1 Zero truncated power series distribution6.5.2 Left truncated power series distribution; 6.6 Reference notes; 6.7 Exercises and complements; 7 COMPOUND AND MIXTURE DISTRIBUTIONS; 7.1 Introduction; 7.2 Compound discrete distributions; 7.3 Mixture discrete distributions; 7.4 Particular compounding distributions; 7.4.1 Poisson compounding distribution; 7.4.2 Binomial compounding distribution; 7.4.3 Negative binomial compounding distribution; 7.4.4 Logarithmic compounding distribution; 7.5 Compound Poisson distributions; 7.5.1 Hermite distribution; 7.5.2 Generalized Hermite distribution 7.5.3 Pólya-Aeppli distribution |
| Record Nr. | UNINA-9910143581703321 |
|
Charalambides Ch. A
|
||
| Hoboken, N.J., : Wiley-Interscience, c2005 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Combinatorial methods in discrete distributions [[electronic resource] /] / Charalambos A. Charalambides
| Combinatorial methods in discrete distributions [[electronic resource] /] / Charalambos A. Charalambides |
| Autore | Charalambides Ch. A |
| Pubbl/distr/stampa | Hoboken, N.J., : Wiley-Interscience, c2005 |
| Descrizione fisica | 1 online resource (440 p.) |
| Disciplina |
511.6
519.2/4 519.24 |
| Collana | Wiley series in probability and statistics |
| Soggetto topico |
Combinatorial analysis
Distribution (Probability theory) |
| ISBN |
1-280-27703-3
9786610277032 0-470-32376-0 0-471-73318-0 0-471-73317-2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
COMBINATORIAL METHODS IN DISCRETE DISTRIBUTIONS; Contents; Preface; 1 BASIC COMBINATORICS AND PROBABILITY; 1.1 Basic counting principles; 1.2 Recurrence relations; 1.3 Finite differences; 1.4 Discrete probability; 1.5 Inclusion and exclusion principle; 1.6 Distributions and moments of random variables; 1.7 Generating functions; 1.8 Reference notes; 1.9 Exercises and complements; 2 STIRLING NUMBERS; 2.1 Introduction; 2.2 Definitions and generating functions; 2.3 Explicit expressions and recurrence relations; 2.4 Generalized factorial coefficients
2.5 Enumeration of partitions by subsets and permutations by cycles2.6 Reference notes; 2.7 Exercises and complements; 3 GENERALIZED STIRLING AND LAH NUMBERS; 3.1 Introduction; 3.2 Associated Stirling numbers; 3.3 Associated generalized factorial coefficients; 3.4 Universal generating functions; 3.5 Generalized Stirling numbers; 3.6 Generalized Lah numbers; 3.7 Reference notes; 3.8 Exercises and complements; 4 OCCUPANCY DISTRIBUTIONS; 4.1 Introduction; 4.2 A random occupancy model; 4.3 Occupancy distributions; 4.4 Particular occupancy distributions; 4.4.1 Classical occupancy distribution 4.4.2 Restricted occupancy distribution4.4.3 Pseudo-contagious occupancy distribution; 4.4.4 Restricted Bose-Einstein occupancy distribution; 4.5 Statistical applications; 4.6 A general random occupancy model; 4.7 Reference notes; 4.8 Exercises and complements; 5 SEQUENTIAL OCCUPANCY DISTRIBUTIONS; 5.1 Introduction; 5.2 A sequential random occupancy model; 5.3 Sequential occupancy distributions; 5.4 Particular sequential occupancy distributions; 5.4.1 Sequential classical occupancy distributions; 5.4.2 Sequential restricted occupancy distributions 5.4.3 Sequential pseudo-contagious occupancy distributions5.5 Statistical applications; 5.6 A reduced sequential occupancy model; 5.7 Reference notes; 5.8 Exercises and complements; 6 CONVOLUTIONS OF TRUNCATED DISTRIBUTIONS; 6.1 Introduction; 6.2 Zero truncated discrete distributions; 6.3 Some particular convolutions; 6.3.1 Zero truncated Poisson distribution; 6.3.2 Logarithmic distribution; 6.3.3 Zero truncated binomial distribution; 6.3.4 Zero truncated negative binomial distribution; 6.4 General truncated discrete distributions; 6.5 Statistical applications 6.5.1 Zero truncated power series distribution6.5.2 Left truncated power series distribution; 6.6 Reference notes; 6.7 Exercises and complements; 7 COMPOUND AND MIXTURE DISTRIBUTIONS; 7.1 Introduction; 7.2 Compound discrete distributions; 7.3 Mixture discrete distributions; 7.4 Particular compounding distributions; 7.4.1 Poisson compounding distribution; 7.4.2 Binomial compounding distribution; 7.4.3 Negative binomial compounding distribution; 7.4.4 Logarithmic compounding distribution; 7.5 Compound Poisson distributions; 7.5.1 Hermite distribution; 7.5.2 Generalized Hermite distribution 7.5.3 Pólya-Aeppli distribution |
| Record Nr. | UNINA-9910830739403321 |
|
Charalambides Ch. A
|
||
| Hoboken, N.J., : Wiley-Interscience, c2005 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Combinatorial methods in discrete distributions [[electronic resource] /] / Charalambos A. Charalambides
| Combinatorial methods in discrete distributions [[electronic resource] /] / Charalambos A. Charalambides |
| Autore | Charalambides Ch. A |
| Pubbl/distr/stampa | Hoboken, N.J., : Wiley-Interscience, c2005 |
| Descrizione fisica | 1 online resource (440 p.) |
| Disciplina |
511.6
519.2/4 519.24 |
| Collana | Wiley series in probability and statistics |
| Soggetto topico |
Combinatorial analysis
Distribution (Probability theory) |
| ISBN |
1-280-27703-3
9786610277032 0-470-32376-0 0-471-73318-0 0-471-73317-2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
COMBINATORIAL METHODS IN DISCRETE DISTRIBUTIONS; Contents; Preface; 1 BASIC COMBINATORICS AND PROBABILITY; 1.1 Basic counting principles; 1.2 Recurrence relations; 1.3 Finite differences; 1.4 Discrete probability; 1.5 Inclusion and exclusion principle; 1.6 Distributions and moments of random variables; 1.7 Generating functions; 1.8 Reference notes; 1.9 Exercises and complements; 2 STIRLING NUMBERS; 2.1 Introduction; 2.2 Definitions and generating functions; 2.3 Explicit expressions and recurrence relations; 2.4 Generalized factorial coefficients
2.5 Enumeration of partitions by subsets and permutations by cycles2.6 Reference notes; 2.7 Exercises and complements; 3 GENERALIZED STIRLING AND LAH NUMBERS; 3.1 Introduction; 3.2 Associated Stirling numbers; 3.3 Associated generalized factorial coefficients; 3.4 Universal generating functions; 3.5 Generalized Stirling numbers; 3.6 Generalized Lah numbers; 3.7 Reference notes; 3.8 Exercises and complements; 4 OCCUPANCY DISTRIBUTIONS; 4.1 Introduction; 4.2 A random occupancy model; 4.3 Occupancy distributions; 4.4 Particular occupancy distributions; 4.4.1 Classical occupancy distribution 4.4.2 Restricted occupancy distribution4.4.3 Pseudo-contagious occupancy distribution; 4.4.4 Restricted Bose-Einstein occupancy distribution; 4.5 Statistical applications; 4.6 A general random occupancy model; 4.7 Reference notes; 4.8 Exercises and complements; 5 SEQUENTIAL OCCUPANCY DISTRIBUTIONS; 5.1 Introduction; 5.2 A sequential random occupancy model; 5.3 Sequential occupancy distributions; 5.4 Particular sequential occupancy distributions; 5.4.1 Sequential classical occupancy distributions; 5.4.2 Sequential restricted occupancy distributions 5.4.3 Sequential pseudo-contagious occupancy distributions5.5 Statistical applications; 5.6 A reduced sequential occupancy model; 5.7 Reference notes; 5.8 Exercises and complements; 6 CONVOLUTIONS OF TRUNCATED DISTRIBUTIONS; 6.1 Introduction; 6.2 Zero truncated discrete distributions; 6.3 Some particular convolutions; 6.3.1 Zero truncated Poisson distribution; 6.3.2 Logarithmic distribution; 6.3.3 Zero truncated binomial distribution; 6.3.4 Zero truncated negative binomial distribution; 6.4 General truncated discrete distributions; 6.5 Statistical applications 6.5.1 Zero truncated power series distribution6.5.2 Left truncated power series distribution; 6.6 Reference notes; 6.7 Exercises and complements; 7 COMPOUND AND MIXTURE DISTRIBUTIONS; 7.1 Introduction; 7.2 Compound discrete distributions; 7.3 Mixture discrete distributions; 7.4 Particular compounding distributions; 7.4.1 Poisson compounding distribution; 7.4.2 Binomial compounding distribution; 7.4.3 Negative binomial compounding distribution; 7.4.4 Logarithmic compounding distribution; 7.5 Compound Poisson distributions; 7.5.1 Hermite distribution; 7.5.2 Generalized Hermite distribution 7.5.3 Pólya-Aeppli distribution |
| Record Nr. | UNINA-9910840956703321 |
|
Charalambides Ch. A
|
||
| Hoboken, N.J., : Wiley-Interscience, c2005 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Dirichlet and related distributions : theory, methods and applications / / Kai Wang Ng, Guo-Liang Tian, Man-Lai Tang
| Dirichlet and related distributions : theory, methods and applications / / Kai Wang Ng, Guo-Liang Tian, Man-Lai Tang |
| Autore | Ng Kai Wang |
| Pubbl/distr/stampa | Chichester, England : , : Wiley, , 2011 |
| Descrizione fisica | 1 online resource (338 p.) |
| Disciplina |
515.782
519.2/4 |
| Collana | Wiley Series in Probability and Statistics |
| Soggetto topico |
Distribution (Probability theory)
Dirichlet problem |
| ISBN |
1-283-40560-1
9786613405609 1-119-99841-7 1-119-99586-8 1-119-99578-7 |
| Classificazione | MAT029000 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
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 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 |
| Record Nr. | UNINA-9910130868703321 |
|
Ng Kai Wang
|
||
| Chichester, England : , : Wiley, , 2011 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Dirichlet and related distributions : theory, methods and applications / / Kai Wang Ng, Guo-Liang Tian, Man-Lai Tang
| Dirichlet and related distributions : theory, methods and applications / / Kai Wang Ng, Guo-Liang Tian, Man-Lai Tang |
| Autore | Ng Kai Wang |
| Pubbl/distr/stampa | Chichester, England : , : Wiley, , 2011 |
| Descrizione fisica | 1 online resource (338 p.) |
| Disciplina |
515.782
519.2/4 |
| Collana | Wiley Series in Probability and Statistics |
| Soggetto topico |
Distribution (Probability theory)
Dirichlet problem |
| ISBN |
1-283-40560-1
9786613405609 1-119-99841-7 1-119-99586-8 1-119-99578-7 |
| Classificazione | MAT029000 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
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 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 |
| Record Nr. | UNINA-9910813761303321 |
|
Ng Kai Wang
|
||
| Chichester, England : , : Wiley, , 2011 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Distributions with fixed marginals and related topics
| Distributions with fixed marginals and related topics |
| Pubbl/distr/stampa | [Place of publication not identified], : Institute of Mathematical Statistics, 1996 |
| Disciplina | 519.2/4 |
| Collana | Lecture notes-monograph series Distributions with fixed marginals and related topics |
| Soggetto topico |
Marginal distributions - Congresses
Mathematics Physical Sciences & Mathematics Mathematical Statistics |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910482887603321 |
| [Place of publication not identified], : Institute of Mathematical Statistics, 1996 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Distributions with fixed marginals and related topics
| Distributions with fixed marginals and related topics |
| Pubbl/distr/stampa | [Place of publication not identified], : Institute of Mathematical Statistics, 1996 |
| Disciplina | 519.2/4 |
| Collana | Lecture notes-monograph series Distributions with fixed marginals and related topics |
| Soggetto topico |
Marginal distributions - Congresses
Mathematics Physical Sciences & Mathematics Mathematical Statistics |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISA-996210821503316 |
| [Place of publication not identified], : Institute of Mathematical Statistics, 1996 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
