# On the Exceedances of Exchangeable Random Variables

Satish Iyengar ()
Satish Iyengar: University of Pittsburgh

Sankhya B: The Indian Journal of Statistics, 2021, vol. 83, issue 1, No 3, 26-35

Abstract: 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.

Keywords: Exceedance; latent variables; likelihood ratio; Majorization.; Primary 62E10; 62H05 (search for similar items in EconPapers)
Date: 2021
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