In this chapter, we examine the use of special forms of correlated random e ects in the generalized linear mixed model (GLMM) setting. A special feature of our GLMM is the inclusion of random residual e ects to account for lack of t due to extra variation, outliers and other unexplained sources of variation. For random e ects, we consider, in particular, the correlation structure and improper p...

It is well known that the Fisher scoring iteration for generalized linear models has the same form as the Gauss-Newton algorithm for normal regression. This note shows that exponential dispersion models are the most general families to preserve this form for the scoring iteration. Therefore exponential dispersion models are the most general extension of generalized linear models for which the a...

Exponential dispersion models, which are linear exponential families with a dispersion parameter, are the prototype response distributions for generalized linear models. The Tweedie families are those exponential dispersion models with power mean-variance relationships. The normal, Poisson, gamma and inverse Gaussian distributions are Tweedie families. Apart from these special cases, Tweedie di...

Several constitutive models have been proposed for description of mechanical behaviour of soft tissues containing collagen fibres. The model with aligned fibres is modified in this paper to take the dispersion of fibre orientations into account through angular integration and it is compared with the model that is defined through generalized structure tensor. The paper is focused on the effect o...

Fitness and fertility traits of dairy cattle are of increasing importance and are often measured on a discrete scale. The development and application of generalized linear mixed models to the genetic analysis of these traits are reviewed. Because current genetic evaluation systems are predominantly based on animal models, the inferential challenges of highly parameterized generalized linear mix...

A new time-fractional derivative with Mittag-Leffler memory kernel, called the generalized Atangana-Baleanu is defined along associated integral operator. Some properties of operators are proved. The operator suitable to generate by particularization known Atangana-Baleanu, Caputo-Fabrizio and Caputo derivatives. mathematical model advection-dispersion process kinetic adsorption formulated cons...

We study the generalized Fong–Vasicek two-factor interest rate model with stochastic volatility. In this model dispersion is assumed to follow a non-negative process with volatility proportional to the square root of dispersion, while the drift is assumed to be a general function. We consider averaged bond prices with respect to the limiting distribution of stochastic dispersion. The averaged b...

This paper studies the effect of traffic dispersion on the reduction of the total effective bandwidth requirement. In this paper, we consider a discrete-time queueing system and a particular source model which is called generalized binary Markov source (GBMS). We then focus on the effective bandwidth of GBMS. We provide some numerical results to investigate the effect of traffic dispersion on t...