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Generalized Gamma Convolutions and Related Classes of Distributions and Densities [[electronic resource] /] / by Lennart Bondesson
| Generalized Gamma Convolutions and Related Classes of Distributions and Densities [[electronic resource] /] / by Lennart Bondesson |
| Autore | Bondesson Lennart |
| Edizione | [1st ed. 1992.] |
| Pubbl/distr/stampa | New York, NY : , : Springer New York : , : Imprint : Springer, , 1992 |
| Descrizione fisica | 1 online resource (XIV, 585 p.) |
| Disciplina | 519.2/4 |
| Collana | Lecture Notes in Statistics |
| Soggetto topico |
Applied mathematics
Engineering mathematics Applications of Mathematics |
| ISBN | 1-4612-2948-0 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | 1. Introduction and Summary -- 1.1 Introduction -- 1.2 Summary -- 1.3 General remarks and notation -- 2. Basic Concepts and Facts -- 2.1 Some facts from probability theory -- 2.2 Particular probability distributions -- 2.3 Infinite divisibility -- 2.4 Pick functions and some applications -- 2.5 Some complementary results -- 3. Generalized Gamma Convolutions -- 3.1 Definition and basic theory -- 3.2 Examples of distributions in ? -- 3.3 A composition theorem -- 3.4 Two real characterizations of the mgf of a GGC -- 3.5 Widened GGC’s -- 3.6 Bivariate GGC’s -- 3.7 Complementary results and notes -- 4. Densities of Generalized Gamma Convolutions -- 4.1 GGC’s as mixtures of Gamma distributions -- 4.2 A class of mixtures of Exponential distributions in ? -- 4.3 A fundamental class of densities in ? -- 4.4 A multiplicative property of GGC’s -- 4.5 Complementary results and notes -- 5. Hyperbolically Completely Monotone Densities -- 5.1 The class b -- 5.2 The ?-class -- 5.3 A surprise and its consequences -- 5.4 Decreasing HCM-functions -- 5.5 Creation of new densities in ? by composition -- 5.6 Multiplication of ?-variables -- 5.7 ?-distributions with explicit Laplace transforms -- 5.8 Complementary results and notes -- 6. Back to ? -- 6.1 Real characterizations of some transforms -- 6.2 Multiplicative properties of ? -- 6.3 Some nested subclasses of ? and their properties -- 6.4 Summary and a new perspective -- 6.5 Complementary results and notes -- 7. Extended Generalized Gamma Convolutions -- 7.1 Definition and basic theory -- 7.2 Examples -- 7.3 EGGC’s as variance mixtures of the Normal distribution -- 7.4 More on composition -- 7.5 Self-reciprocal densities -- 7.6 Complementary results and notes -- 8. Generalized Negative Binomial Convolutions -- 8.1 Definition and main properties -- 8.2 Examples of distributions in ?d -- 8.3 In search of a discrete ?-class -- 8.4 Complementary results and notes -- 9. The ?2-class of Distributions -- 9.1 Definition and main properties -- 9.2 Examples of ?2-distributions -- 9.3 First passage time distributions as ?2-distributions -- 9.4 On densities of distributions in ?2 -- 9.5 Extensions -- 9.6 Notes -- 10. Shot-Noise Distributions -- 10.1 Shot-noise processes -- 10.2 Classes of shot-noise distributions on R+ -- 10.3 Discrete shot-noise distributions -- 10.4 Notes -- Final Words -- Author Index. |
| Record Nr. | UNINA-9910480549703321 |
Bondesson Lennart
|
||
| New York, NY : , : Springer New York : , : Imprint : Springer, , 1992 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Generalized Gamma Convolutions and Related Classes of Distributions and Densities [[electronic resource] /] / by Lennart Bondesson
| Generalized Gamma Convolutions and Related Classes of Distributions and Densities [[electronic resource] /] / by Lennart Bondesson |
| Autore | Bondesson Lennart |
| Edizione | [1st ed. 1992.] |
| Pubbl/distr/stampa | New York, NY : , : Springer New York : , : Imprint : Springer, , 1992 |
| Descrizione fisica | 1 online resource (XIV, 585 p.) |
| Disciplina | 519.2/4 |
| Collana | Lecture Notes in Statistics |
| Soggetto topico |
Applied mathematics
Engineering mathematics Applications of Mathematics |
| ISBN | 1-4612-2948-0 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | 1. Introduction and Summary -- 1.1 Introduction -- 1.2 Summary -- 1.3 General remarks and notation -- 2. Basic Concepts and Facts -- 2.1 Some facts from probability theory -- 2.2 Particular probability distributions -- 2.3 Infinite divisibility -- 2.4 Pick functions and some applications -- 2.5 Some complementary results -- 3. Generalized Gamma Convolutions -- 3.1 Definition and basic theory -- 3.2 Examples of distributions in ? -- 3.3 A composition theorem -- 3.4 Two real characterizations of the mgf of a GGC -- 3.5 Widened GGC’s -- 3.6 Bivariate GGC’s -- 3.7 Complementary results and notes -- 4. Densities of Generalized Gamma Convolutions -- 4.1 GGC’s as mixtures of Gamma distributions -- 4.2 A class of mixtures of Exponential distributions in ? -- 4.3 A fundamental class of densities in ? -- 4.4 A multiplicative property of GGC’s -- 4.5 Complementary results and notes -- 5. Hyperbolically Completely Monotone Densities -- 5.1 The class b -- 5.2 The ?-class -- 5.3 A surprise and its consequences -- 5.4 Decreasing HCM-functions -- 5.5 Creation of new densities in ? by composition -- 5.6 Multiplication of ?-variables -- 5.7 ?-distributions with explicit Laplace transforms -- 5.8 Complementary results and notes -- 6. Back to ? -- 6.1 Real characterizations of some transforms -- 6.2 Multiplicative properties of ? -- 6.3 Some nested subclasses of ? and their properties -- 6.4 Summary and a new perspective -- 6.5 Complementary results and notes -- 7. Extended Generalized Gamma Convolutions -- 7.1 Definition and basic theory -- 7.2 Examples -- 7.3 EGGC’s as variance mixtures of the Normal distribution -- 7.4 More on composition -- 7.5 Self-reciprocal densities -- 7.6 Complementary results and notes -- 8. Generalized Negative Binomial Convolutions -- 8.1 Definition and main properties -- 8.2 Examples of distributions in ?d -- 8.3 In search of a discrete ?-class -- 8.4 Complementary results and notes -- 9. The ?2-class of Distributions -- 9.1 Definition and main properties -- 9.2 Examples of ?2-distributions -- 9.3 First passage time distributions as ?2-distributions -- 9.4 On densities of distributions in ?2 -- 9.5 Extensions -- 9.6 Notes -- 10. Shot-Noise Distributions -- 10.1 Shot-noise processes -- 10.2 Classes of shot-noise distributions on R+ -- 10.3 Discrete shot-noise distributions -- 10.4 Notes -- Final Words -- Author Index. |
| Record Nr. | UNINA-9910789223603321 |
|
Bondesson Lennart
|
||
| New York, NY : , : Springer New York : , : Imprint : Springer, , 1992 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||