This vignette describes the R hglm package via a series of applications that may be of interest to applied scientists. The hglm package implements the estimation algorithm for hierarchical generalized linear models. The package fits generalized linear models with random effects, where the random effect may come from a conjugate exponential-family distribution (Gaussian, Gamma, Beta or inverse-G...

Approximate equations are derived for the amount of information a nerve cell or group of nerve cells can transmit about a stimulus of a given duration using a frequency code (i.e., assuming the mean frequency of nerve impulses measures the intensity of a maintained stimulus). The equations take into account the variability of successive interspike intervals, and any serial correlations between ...

UNLABELLED In this paper, we propose a five-parameter lifetime model called the McDonald exponentiated gamma distribution to extend beta exponentiated gamma, Kumaraswamy exponentiated gamma and exponentiated gamma, among several other models. We provide a comprehensive mathematical treatment of this distribution. We derive the moment generating function and the rth moment. We discuss estimation...

In vivo cortical neurons are known to exhibit highly irregular spike patterns. Because the intervals between successive spikes fluctuate greatly, irregular neuronal firing makes it difficult to estimate instantaneous firing rates accurately. If, however, the irregularity of spike timing is decoupled from rate modulations, the estimate of firing rate can be improved. Here, we introduce a novel c...

We study the stationary distribution of the number of busy servers in a GI/GI/∞ system in which the service-time distribution is identical to the interarrival-time distribution, and obtain several representations for the variance. As a result we can verify an expression for the variance, conjectured by Rajaratnam and Takawira (IEEE Trans. Vehicular Technol. 50 (2001) 954-970), when the common d...

In modeling internet traffic there have been little attention on skewness. Shifted gamma distribution is a simple traffic model which is long-range dependent and its marginal distribution exhibits specific skewness. Using this model, we give some analytical results on the impact of skewness on the queueing performance such as mean delay and overflow probability. We also investigate the feasibil...

Heterogeneity is an important property of any population experiencing a disease. Here we apply general methods of the theory of heterogeneous populations to the simplest mathematical models in epidemiology. In particular, an SIR (susceptible-infective-removed) model is formulated and analyzed when susceptibility to or infectivity of a particular disease is distributed. It is shown that a hetero...

The problem of estimating the parameters in a generalized linear model when a covariate is subject to censoring is studied. A newmethod based on an estimating function approach is proposed. The method does not assume a parametric form for the distribution of the response given the regressors and is computationally simple. In the linear regression case, the proposed approach implies the use of m...

A mathematical formulation is developed for systematic tracking of the random movement of a mobile station in a cellular environment. It incorporates mobility parameters under the most generalized conditions, so that the model can be tailored to be applicable in most cellular environments. This mobility model is used to characterize different mobility-related traffic parameters in cellular syst...

Frequency analysis of hydrometeorological extremes plays an important role in the design of hydraulic structures. A multitude of distributions have been employed for hydrological frequency analysis, and more than one distribution is often found to be adequate for frequency analysis. The current method for selecting the best fitted distributions are not so objective. Using different kinds of con...