Finite mixtures of (multivariate) Gaussian distributions have broad utility, including their usage for model-based clustering. There is increasing recognition of mixtures of asymmetric distributions as powerful alternatives to traditional mixtures of Gaussian and mixtures of t distributions. The present work contributes to that assertion by addressing some facets of estimation and inference for mixtures-of-gamma distributions, including in the context of model-based clustering. Maximum likelihood estimation of mixtures of gammas is performed using an expectation–conditional–maximization (ECM) algorithm. The Wilson–Hilferty normal approximation is employed as part of an effective starting value strategy for the ECM algorithm, as well as provides insight into an effective model-based clustering strategy. Inference regarding the appropriateness of a common-shape mixture-of-gammas distribution is motivated by theory from research on infant habituation. We provide extensive simulation results that demonstrate the strong performance of our routines as well as analyze two real data examples: an infant habituation dataset and a whole genome duplication dataset.

中文翻译：

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有限的伽玛混合分布：估计，推断和基于模型的聚类

（多元）高斯分布的有限混合具有广泛的用途，包括其在基于模型的聚类中的使用。人们越来越认识到，不对称分布的混合物是传统高斯混合物和t混合物的有力替代品分布。本工作通过解决γ混合分布的估计和推断的某些方面，包括在基于模型的聚类中，为该主张做出了贡献。使用期望-条件-最大化（ECM）算法执行伽马混合的最大似然估计。Wilson-Hilferty正态近似被用作ECM算法的有效起始值策略的一部分，并提供了对基于模型的有效聚类策略的洞察力。从婴儿习惯研究的理论出发，得出关于同形游戏混合分布的适当性的推论。我们提供了广泛的模拟结果，这些结果证明了例程的强大性能，并分析了两个真实的数据示例：