Annals of Applied Probability

On the unique crossing conjecture of Diaconis and Perlman on convolutions of gamma random variables

Yaming Yu

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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 $\alpha\geq1$.

Article information

Source
Ann. Appl. Probab., Volume 27, Number 6 (2017), 3893-3910.

Dates
Received: July 2016
Revised: April 2017
First available in Project Euclid: 15 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1513328716

Digital Object Identifier
doi:10.1214/17-AAP1304

Mathematical Reviews number (MathSciNet)
MR3737940

Zentralblatt MATH identifier
1382.60045

Subjects
Primary: 60E15: Inequalities; stochastic orderings

Keywords
Convolution log-concavity majorization tail probability total positivity; unimodality

Citation

Yu, Yaming. On the unique crossing conjecture of Diaconis and Perlman on convolutions of gamma random variables. Ann. Appl. Probab. 27 (2017), no. 6, 3893--3910. doi:10.1214/17-AAP1304. https://projecteuclid.org/euclid.aoap/1513328716


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