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On the Exceedances of Exchangeable Random Variables

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  • Satish Iyengar

    (University of Pittsburgh)

Abstract

Suppose that Xn = (X1,…,Xn) have mean 0, and a single-factor covariance Σ = (σij) with σii = 1 and σij = ρ ≥ 0 for i ≠ j. For a threshold c, let Sn be the number of components of Xn that exceed c. We express the distribution of Sn in terms of a single integral, provide the limiting distribution as n → ∞ $n \rightarrow \infty $ , and show that the limit resembles the Beta family. We then describe the shape of the exceedance distribution when the underlying distributions of the single-factor model have a certain likelihood ratio criterion with respect to its scale parameter, and we show that it obeys a majorization ordering.

Suggested Citation

  • Satish Iyengar, 2021. "On the Exceedances of Exchangeable Random Variables," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(1), pages 26-35, May.
    • Handle: RePEc:spr:sankhb:v:83:y:2021:i:1:d:10.1007_s13571-021-00252-3
    DOI: 10.1007/s13571-021-00252-3
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