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One characterization of symmetry

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  • Ushakov, N.G.

Abstract

In this note we present one characterization of symmetry of probability distributions in Euclidean spaces which is formulated as follows. Let X and Y be independent and identically distributed random elements in a separable Euclidean space E. If EehX 0, then the distribution of X is symmetric if and only if E(X-Y,t)p=E(X+Y,t)p for some 0

Suggested Citation

  • Ushakov, N.G., 2011. "One characterization of symmetry," Statistics & Probability Letters, Elsevier, vol. 81(5), pages 614-617, May.
    • Handle: RePEc:eee:stapro:v:81:y:2011:i:5:p:614-617
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    References listed on IDEAS

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    1. Ramachandran, B., 1997. "Characteristic functions with some powers real -- III," Statistics & Probability Letters, Elsevier, vol. 34(1), pages 33-36, May.
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    Cited by:

    1. Vexler, Albert & Zou, Li, 2022. "Linear projections of joint symmetry and independence applied to exact testing treatment effects based on multidimensional outcomes," Journal of Multivariate Analysis, Elsevier, vol. 190(C).
    2. Ahmadi, Jafar, 2020. "Characterization results for symmetric continuous distributions based on the properties of k-records and spacings," Statistics & Probability Letters, Elsevier, vol. 162(C).

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