ON THE UNIQUE CROSSING CONJECTURE OF DIACONIS AND PERLMAN ON CONVOLUTIONS OF GAMMA RANDOM VARIABLES

• 成果类型: Article
• 署名作者: Yu, Yaming
• 署名单位: University of California System; University of California Irvine
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/17-AAP1304
• 发表日期: 2017
• 页码: 3893-3910
• 关键词: linear-combinations; extremal probabilities; inequalities

摘要

Diaconis and Perlman [In Topics in Statistical Dependence (Somerset, PA, 1987) (1990) 147-166, IMS] conjecture that the distribution functions of two weighted sums of i.i.d. gamma random variables cross exactly once if one weight vector majorizes the other. We disprove this conjecture when the shape parameter of the gamma variates is alpha < 1 and prove it when alpha >= 1.