The information divergence of a probability measure P from an exponential family E over a nite set is deened as innmum of the divergences of P from Q subject to Q in E. For convex exponential families the local maximizers of this function of P are found. General exponential family E of dimension d is enlarged to an exponential family E of the dimension at most 3d + 2 such that the local maximiz...

In this paper we have proposed a class of Generalized Autoregressive Moving Average (GARMA) models which extend univariate ARMA models to a non-Gaussian situation (i.e. they extend the univariate Generalized Linear Model to incorporate time dependence in the observations). The simplicity of the tting algorithm within the iteratively reweighted least squares (IRLS) framework will be shown. Model...

This article describes the evolution of applied exponential family models, starting at 1972, the year of publication of the seminal papers on generalized linear models and on Cox regression, and leading to multivariate (i) marginal models and inference based on estimating equations and (ii) random effects models and Bayesian simulation-based posterior inference. By referring to recent work in g...

In this paper we consider both the dynamical and parameter planes for the complex exponential family Eλ(z) = λez where the parameter λ is complex. We show that there are infinitely many curves or “hairs” in the dynamical plane that contain points whose orbits underEλ tend to infinity and hence are in the Julia set. We also show that there are similar hairs in the λ-plane. In this case, the hair...