2020/03/29 by Reinaldo B. Arellano‐Valle, Reinaldo B. Arellano-Valle, Adelchi Azzalini +2
Decision Sciences · Engineering · Mathematics · #Diverse Scientific and Engineering Research #FOS: Mathematics #Optimal Experimental Design Methods #Probability (math.PR) #Statistical Distribution Estimation and Applications #Statistics Theory (math.ST) #math.PR #math.ST #stat.TH
paper · pdf · doi:10.48550/arxiv.2003.13076
arxiv created 2020/03/29 · openalex publication_date 2020/03/29 · arxiv updated 2020/03/31 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
Several formulations have long existed in the literature in the form of continuous mixtures of normal variables where a mixing variable operates on the mean or on the variance or on both the mean and the variance of a multivariate normal variable, by changing the nature of these basic constituents from constants to random quantities. More recently, other mixture-type constructions have been introduced, where the core random component, on which the mixing operation operates, is not necessarily normal. The main aim of the present work is to show that many existing constructions can be encompassed by a formulation where normal variables are mixed using two univariate random variables. For this formulation, we derive various general properties. Within the proposed framework, it is also simpler to formulate new proposals of parametric families and we provide a few such instances. At the same time, the exposition provides a review of the theme of normal mixtures.