We propose a new technique for the study of multivariate count data. The proposed model is applied to the study of the number of individuals several fossil species found in a set of geographical observation points. First, we are proposing a multivariate model based on the Poisson distributions, which allows positive and negative correlations between the components. We are extending the log-linear Poisson model in the multivariate case through the conditional distributions. For this model, we obtain the maximum likelihood estimates and compute several goodness of fit statistics. Finally we illustrate the application of the proposed method over data sets: various simulated data sets and a count data set of various fossil species.

我们提出了一种用于研究多变量计数数据的新技术。所提出的模型应用于研究在一组地理观测点中发现的几种化石物种的个体数量。首先，我们提出了一个基于泊松分布的多元模型，它允许组件之间存在正相关和负相关。我们正在通过条件分布在多元情况下扩展对数线性泊松模型。对于这个模型，我们获得最大似然估计并计算几个拟合优度统计量。最后，我们说明了该方法在数据集上的应用：各种模拟数据集和各种化石物种的计数数据集。