The variance upper bound for a mixed random variable
Resumen:
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 necessary need to be symmetric and is multimodal. We also characterize the cases when these bounds are optimal.
| 2017 | |
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Gruss’ inequality Popoviciu’s inequality Unimodal Symmetry |
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| Inglés | |
| Universidad de Montevideo | |
| REDUM | |
| https://hdl.handle.net/20.500.12806/1359 | |
| Acceso abierto | |
| Attribution-NonCommercial-NoDerivatives 4.0 Internacional |
| Sumario: | 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 necessary need to be symmetric and is multimodal. We also characterize the cases when these bounds are optimal. |
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