We introduce some new indexes to measure the departure of any multivariate continuous distribution on the nonnegative orthant of the corresponding space from a given reference distribution. The reference distribution may be an uncorrelated exponential model. The proposed multivariate variation indexes that are a continuous analogue to the relative Fisher dispersion indexes of multivariate count models are also scalar quantities, defined as ratios of two quadratic forms of the mean vector to the covariance matrix. They can be used to discriminate between continuous positive distributions. Generalized and multiple marginal variation indexes with and without correlation structure, respectively, and their relative extensions are discussed. The asymptotic behaviors and other properties are studied. Illustrative examples as well as numerical applications are analyzed under several scenarios, leading to appropriate choices of multivariate models. Some concluding remarks and possible extensions are made.

中文翻译：

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$$ [0，\ infty）^ k $$ [0，∞）k和扩展上的多元连续分布的相对变化指数

我们引入了一些新指标来衡量给定参考分布中对应空间的非负正割上的任何多元连续分布的偏离。参考分布可以是不相关的指数模型。所提出的与多元计数模型的相对Fisher分散指数连续模拟的多元变异指数也是标量，定义为均值向量的两个二次形式与协方差矩阵的比率。它们可以用来区分连续的正分布。分别讨论了具有和不具有相关结构的广义和多个边际变异指数及其相对扩展。研究了渐近行为和其他性质。说明性的例子以及数字应用在几种情形分析，导致适当的多变量模型的选择。进行了一些总结性说明和可能的扩展。