Sequences of elliptical distributions and mixtures of normal distributions. (English) Zbl 1085.62057
Summary: Two conditions are shown under which elliptical distributions are scale mixtures of normal distributions with respect to probability distributions. The issue of finding the mixing distribution function is also considered. As a unified theoretical framework, it is also shown that any scale mixture of normal distributions is always a term of a sequence of elliptical distributions, increasing in dimension, and that all the terms of this sequence are also scale mixtures of normal distributions sharing the same mixing distribution function. Some examples are shown as applications of these concepts, showing the way of finding the mixing distribution function.
MSC:
| 62H05 | Characterization and structure theory for multivariate probability distributions; copulas |
| 62F15 | Bayesian inference |
| 62E10 | Characterization and structure theory of statistical distributions |
Keywords:
Bayesian methods; Elliptically contoured distribution; Elliptical distribution; Laplace transform; Scale mixtures of normal distributionsReferences:
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