The variance upper bound for a mixed random variable

Martín Egozcue and Luis Fuentes García

Communications in Statistics - Theory and Methods, 2018, vol. 47, issue 22, 5391-9395

Abstract: In this note, we derive upper bounds on the variance of a mixed random variable. Our results are an extension of previous results for unimodal and symmetric random variables. The novelty of our findings is that this mixed random variable does not necessarily need to be symmetric and is multimodal. We also characterize the cases when these bounds are optimal.

Date: 2018
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DOI: 10.1080/03610926.2017.1390136

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