Abstract

For two vast families of mixture distributions and a given prior, we provide unified representations of posterior and predictive distributions. Model applications presented include bivariate mixtures of Gamma distributions labeled as Kibble-type, non-central Chi-square and F distributions, the distribution of R² in multiple regression, variance mixture of normal distributions, and mixtures of location-scale exponential distributions including the multivariate Lomax distribution. An emphasis is also placed on analytical representations and the relationships with a host of existing distributions and several hypergeometric functions of one or two variables.

摘要

对于混合分布的两大类和给定的先验，我们提供了后验分布和预测分布的统一表示。提出的模型应用包括标记为 Kibble 型的 Gamma 分布的双变量混合、非中心卡方和 F 分布、多元回归中R ²的分布、正态分布的方差混合以及位置尺度指数分布的混合，包括多元 Lomax 分布。重点还放在分析表示以及与许多现有分布的关系以及一个或两个变量的几个超几何函数上。