Author | Bondesson, Lennart. author |
---|---|
Title | Generalized Gamma Convolutions and Related Classes of Distributions and Densities [electronic resource] / by Lennart Bondesson |
Imprint | New York, NY : Springer New York, 1992 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-2948-3 |
Descript | XIV, 585 p. online resource |
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 GGCโs -- 3.6 Bivariate GGCโs -- 3.7 Complementary results and notes -- 4. Densities of Generalized Gamma Convolutions -- 4.1 GGCโs 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 GGCโs -- 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 EGGCโs 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