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A note on conditional variance and characterization of probability distributions

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  • Jaworski, Piotr
  • Pitera, Marcin

Abstract

In this note we prove a novel characterization result stating that any distribution is determined uniquely up to an additive constant by its conditional variance function where the conditioning is based on double quantile trimming. We also outline potential statistical applications of the proposed characterization.

Suggested Citation

  • Jaworski, Piotr & Pitera, Marcin, 2020. "A note on conditional variance and characterization of probability distributions," Statistics & Probability Letters, Elsevier, vol. 163(C).
    • Handle: RePEc:eee:stapro:v:163:y:2020:i:c:s0167715220301036
    DOI: 10.1016/j.spl.2020.108800
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    References listed on IDEAS

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    1. J. Ruiz & J. Navarro, 1996. "Characterizations based on conditional expectations of the doubled truncated distribution," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 48(3), pages 563-572, September.
    2. Samia El-Arishy, 2005. "A conditional variance characterization of some discrete probability distributions," Statistical Papers, Springer, vol. 46(1), pages 31-45, January.
    3. Piotr Jaworski & Marcin Pitera, 2017. "A note on conditional covariance matrices for elliptical distributions," Papers 1703.00918, arXiv.org.
    4. Jaworski, Piotr & Pitera, Marcin, 2017. "A note on conditional covariance matrices for elliptical distributions," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 230-235.
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    Citations

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    Cited by:

    1. Marcin Pitera & Aleksei Chechkin & Agnieszka Wyłomańska, 2022. "Goodness-of-fit test for $$\alpha$$ α -stable distribution based on the quantile conditional variance statistics," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 31(2), pages 387-424, June.

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