Extended negative binomial hurdle models

Poisson models are widely used for statistical inference on count data. However, zero-inflation or zero-deflation with either overdispersion or underdispersion could occur. Currently, there is no available model for count data, that allows excessive occurrence of zeros along with underdispersion in non-zero counts, even though there have been reported necessity of such models. Furthermore, given an excessive zero rate, we need a model that allows a larger degree of overdispersion than existing models. In this paper, we use a random-effect model to produce a general statistical model for accommodating such phenomenon occurring in real data analyses.

An empirical model for underdispersed count data

We present a novel distribution for modelling count data that are underdispersed relative to the Poisson distribution. The distribution is a form of weighted Poisson distribution and is shown to have advantages over other weighted Poisson distributions that have been proposed to model underdispersion. One key difference is that the weights in our distribution are centred on the mean of the underlying Poisson distribution. Several illustrative examples are presented that illustrate the consistently good performance of the distribution.

Ionic regulation of egg activation

Developing cells have constantly to make decisions: when to proliferate and divide, when and how to differentiate. It is an increasingly attractive idea that these decisions involve changes in intracellular cation concentrations. Our ideas about the mechanisms of changes in intracellular cations come largely from the application of biophysical techniques in the study of excitable tissues. These ideas are proving very valuable to the investigation of the control of proliferation and cell development and it is evident that the ionic mechanisms which pertain in nerve and muscle have their counterparts in other cells. Just as alterations in intracellular ion concentrations serve a signalling function in excitable tissue, so too they act as signals during development. Since almost all the quantitative data on the ionic mechanisms of fertilization come from work on sea urchins we have confined our review to sea urchin eggs.