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July 2002 Limit laws of modulus trimmed sums
Philip S. Griffin, Fozia S. Qazi
Ann. Probab. 30(3): 1466-1485 (July 2002). DOI: 10.1214/aop/1029867133
Let $X,X_1,X_2,\ldots$ be a sequence of independent and identically distributed random variables. Let $ ^{(1)}X_n,\ldots,{^{(n)}X}_n$ be an arrangement of $X_1$, $X_2,\ldots,X_n $ in decreasing order of magnitude, and set ${^{(r_n)}S}_n= {}^{(r_{n}+1)}X_n+\cdots + {^{(n)}X}_{n}$. This is known as the modulus trimmed sum. We obtain a complete characterization of the class of limit laws of the normalized modulus trimmed sum when the underlying distribution is symmetric and $ r_n \to \infty$, $r_nn^{-1}\to 0$.
Philip S. Griffin. Fozia S. Qazi. "Limit laws of modulus trimmed sums." Ann. Probab. 30 (3) 1466 - 1485, July 2002. https://doi.org/10.1214/aop/1029867133
First available in Project Euclid: 20 August 2002
MathSciNet: MR1920273
Digital Object Identifier: 10.1214/aop/1029867133
Primary: 60F05
Keywords: limit laws, Stable laws, Trimmed sum
Rights: Copyright © 2002 Institute of Mathematical Statistics
Ann. Probab.
Vol.30 • No. 3 • July 2002
Philip S. Griffin, Fozia S. Qazi "Limit laws of modulus trimmed sums," The Annals of Probability, Ann. Probab. 30(3), 1466-1485, (July 2002)