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首页> 外文期刊>Journal of applied statistics >Bivariate Negative Binomial Generalized Linear Models for Environmental Count Data
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Bivariate Negative Binomial Generalized Linear Models for Environmental Count Data

机译：环境计数数据的二元负二项式广义线性模型

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摘要

We propose a new bivariate negative binomial model with constant correlation structure, which was derived from a contagious bivariate distribution of two independent Poisson mass functions, by mixing the proposed bivariate gamma type density with constantly correlated covariance structure (Iwasaki & Tsubaki, 2005), which satisfies the integrability condition of McCullagh & Nelder (1989, p. 334). The proposed bivariate gamma type density comes from a natural exponential family. Joe (1997) points out the necessity of a multivariate gamma distribution to derive a multivariate distribution with negative binomial margins, and the luck of a convenient form of multivariate gamma distribution to get a model with greater flexibility in a dependent structure with indices of dispersion. In this paper we first derive a new bivariate negative binomial distribution as well as the first two cumulants, and, secondly, formulate bivariate generalized linear models with a constantly correlated negative binomial covariance structure in addition to the moment estimator of the components of the matrix. We finally fit the bivariate negative binomial models to two correlated environmental data sets.
机译：我们提出了一种新的具有恒定相关结构的双变量负二项式模型，该模型是通过将两个独立的泊松质量函数的传染性双变量分布与建议的双变量伽玛类型密度与恒定相关的协方差结构混合而得到的（Iwasaki＆Tsubaki，2005）。满足McCullagh＆Nelder（1989，p。334）的可积性条件。拟议的双变量伽玛类型密度来自自然指数族。 Joe（1997）指出，必须使用多元伽马分布来导出具有负二项式边际的多元分布，并需要一种便利形式的多元伽马分布来获得在具有色散指数的从属结构中具有更大灵活性的模型。在本文中，我们首先导出一个新的二元负二项式分布以及前两个累积量，其次，除了矩阵成分的矩估计量外，还建立一个具有恒定相关负二项式协方差结构的二元广义线性模型。我们最终将双变量负二项式模型拟合到两个相关的环境数据集。

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