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December 2017 On the unique crossing conjecture of Diaconis and Perlman on convolutions of gamma random variables
Yaming Yu
Ann. Appl. Probab. 27(6): 3893-3910 (December 2017). DOI: 10.1214/17-AAP1304

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 $\alpha<1$ and prove it when $\alpha\geq1$.

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Yaming Yu. "On the unique crossing conjecture of Diaconis and Perlman on convolutions of gamma random variables." Ann. Appl. Probab. 27 (6) 3893 - 3910, December 2017. https://doi.org/10.1214/17-AAP1304

Information

Received: 1 July 2016; Revised: 1 April 2017; Published: December 2017
First available in Project Euclid: 15 December 2017

zbMATH: 1382.60045
MathSciNet: MR3737940
Digital Object Identifier: 10.1214/17-AAP1304

Subjects:
Primary: 60E15

Rights: Copyright © 2017 Institute of Mathematical Statistics

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Vol.27 • No. 6 • December 2017
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