2020/03/29 by Reinaldo B. Arellano‐Valle, Adelchi Azzalini, Arellano-Valle, Reinaldo B. +1
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)
paper · pdf · doi:10.48550/arxiv.2003.13076
openalex publication_date 2020/03/29 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
Several formulations have long existed in the literature in the form of\ncontinuous mixtures of normal variables where a mixing variable operates on the\nmean or on the variance or on both the mean and the variance of a multivariate\nnormal variable, by changing the nature of these basic constituents from\nconstants to random quantities. More recently, other mixture-type constructions\nhave been introduced, where the core random component, on which the mixing\noperation operates, is not necessarily normal. The main aim of the present work\nis to show that many existing constructions can be encompassed by a formulation\nwhere normal variables are mixed using two univariate random variables. For\nthis formulation, we derive various general properties. Within the proposed\nframework, it is also simpler to formulate new proposals of parametric families\nand we provide a few such instances. At the same time, the exposition provides\na review of the theme of normal mixtures.\n