<p>Due to their interpretability and relatively straightforward mathematical handling, Gaussian mixture models have been very popular among researchers and practitioners. However, the use of such mixtures can be compromised in the presence of mild outliers and groups with heavy tails. Various techniques to address these concerns have been proposed in the literature, with one prominent approach being to employ a mixture of contaminated normal distributions. Such distributions represent a mixture of two normal components with a common location parameter and one scale parameter being the multiple of the other one. This way, the component with inflated covariances can help model potentially heavy distribution tails. Another popular use of contaminated normal components is to detect mild outliers. In this paper, we discuss the use of contaminated normal distributions in both cases and provide some novel insight on the use of these popular mixtures.</p>

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On the Use of Contaminated Normal Distributions for Modeling Data Groups with Heavy Tails and Outliers

  • Yana Melnykov

摘要

Due to their interpretability and relatively straightforward mathematical handling, Gaussian mixture models have been very popular among researchers and practitioners. However, the use of such mixtures can be compromised in the presence of mild outliers and groups with heavy tails. Various techniques to address these concerns have been proposed in the literature, with one prominent approach being to employ a mixture of contaminated normal distributions. Such distributions represent a mixture of two normal components with a common location parameter and one scale parameter being the multiple of the other one. This way, the component with inflated covariances can help model potentially heavy distribution tails. Another popular use of contaminated normal components is to detect mild outliers. In this paper, we discuss the use of contaminated normal distributions in both cases and provide some novel insight on the use of these popular mixtures.