The Theory of Dispersion ModelsThe theory of dispersion models straddles both statistics and probability, and involves an encyclopedic collection of tools, such as exponential families, asymptotic theory, stochastic processes, Tauber theory, infinite divisibility, and stable distributions. The Theory of Dispersion Models introduces the reader to these models, which serve as error distributions for generalized linear models, and looks at their applications within this context. |
Contents
X | 18 |
Natural exponential families | 37 |
Exponential dispersion models | 71 |
Tweedie models | 127 |
Proper dispersion models | 175 |
References | 219 |
| 226 | |
Common terms and phrases
additive exponential dispersion additive model additive process Barndorff-Nielsen canonical parameter domain Chapter compound Poisson consider convergence results convergence theorem convex support convolution formula corresponding cumulant generating function defined denote deviance residual discrete dispersion parameter duality transformation example Exercise exponential dispersion model func gamma distribution given hence implies infinitely divisible interval inverse Gaussian distribution Jørgensen Lemma Letac mean domain mean value mapping model with unit moment generating function natural exponential family negative binomial distribution normal distribution obtain persion models plots Poisson distribution probability density function probability function Proof proper dispersion model random variable regular of order regular proper dispersion renormalized saddlepoint approximation reproductive exponential dispersion reproductive model scale transformations Show simplex distribution statistical tion Tweedie models unit cumulant function unit variance function v(dy μ² μο σ²