On the unique crossing conjecture of diaconis and perlman on convolutions of gamma random variables

Authors
Yu, Yaming
Citation
Yu, Yaming, On the unique crossing conjecture of diaconis and perlman on convolutions of gamma random variables, Annals of applied probability , 30(6), 2020, pp. 3893-3910
Journal title
Annals of applied probability → ACNP
ISSN journal
10505164
Volume
30
Issue
6
Year of publication
2020
Pages
3893 - 3910
Database
ACNP
SICI code
Abstract
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 . < 1 and prove it when . . 1.