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The variance upper bound for a mixed random variable

Author

Listed:
  • Martín Egozcue
  • Luis Fuentes García

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 necessary need to be symmetric and is multimodal. We also characterize the cases when these bounds are optimal.

Suggested Citation

  • Martín Egozcue & Luis Fuentes García, 2017. "The variance upper bound for a mixed random variable," Documentos de Trabajo/Working Papers 1707, Facultad de Ciencias Empresariales y Economia. Universidad de Montevideo..
    • Handle: RePEc:mnt:wpaper:1707
    as

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    File URL: https://www2.um.edu.uy/fcee_papers/2017/The_variance_upper_bound_for_a_mixed_random_variable.pdf
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    References listed on IDEAS

    as
    1. R. Sharma & R. Bhandari, 2014. "On Variance Upper Bounds for Unimodal Distributions," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 43(21), pages 4503-4513, November.
    2. repec:bla:scandj:v:83:y:1981:i:3:p:419-28 is not listed on IDEAS
    3. Abouammoh, A. M. & Mashhour, A. F., 1994. "Variance upper bounds and convolutions of [alpha]-unimodal distributions," Statistics & Probability Letters, Elsevier, vol. 21(4), pages 281-289, November.
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