Bernoulli

  • Bernoulli
  • Volume 19, Number 5A (2013), 1776-1789.

Some inequalities of linear combinations of independent random variables: II

Xiaoqing Pan, Maochao Xu, and Taizhong Hu

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Abstract

Linear combinations of independent random variables have been extensively studied in the literature. However, most of the work is based on some specific distribution assumptions. In this paper, a companion of (J. Appl. Probab. 48 (2011) 1179–1188), we unify the study of linear combinations of independent nonnegative random variables under the general setup by using some monotone transforms. The results are further generalized to the case of independent but not necessarily identically distributed nonnegative random variables. The main results complement and generalize the results in the literature including (In Studies in Econometrics, Time Series, and Multivariate Statistics (1983) 465–489 Academic Press; Sankhyā Ser. A 60 (1998) 171–175; Sankhyā Ser. A 63 (2001) 128–132; J. Statist. Plann. Inference 92 (2001) 1–5; Bernoulli 17 (2011) 1044–1053).

Article information

Source
Bernoulli, Volume 19, Number 5A (2013), 1776-1789.

Dates
First available in Project Euclid: 5 November 2013

Permanent link to this document
https://projecteuclid.org/euclid.bj/1383661202

Digital Object Identifier
doi:10.3150/12-BEJ429

Mathematical Reviews number (MathSciNet)
MR3129033

Zentralblatt MATH identifier
1284.60046

Keywords
likelihood ratio order log-concavity majorization Schur-concavity usual stochastic order

Citation

Pan, Xiaoqing; Xu, Maochao; Hu, Taizhong. Some inequalities of linear combinations of independent random variables: II. Bernoulli 19 (2013), no. 5A, 1776--1789. doi:10.3150/12-BEJ429. https://projecteuclid.org/euclid.bj/1383661202


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