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Sums of standard uniform random variables

Part of: Distribution theory - Probability Applications

Published online by Cambridge University Press:  01 October 2019

Tiantian Mao ,
Bin Wang  and
Ruodu Wang
Tiantian Mao*
Affiliation:
University of Science and Technology of China
Bin Wang*
Affiliation:
Chinese Academy of Sciences
Ruodu Wang*
Affiliation:
University of Waterloo
*
*Postal address: Department of Statistics and Finance, University of Science and Technology of China, Hefei, Anhui 230026, China. Email address: tmao@ustc.edu.cn
**Postal address: RCSDS, NCMIS, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China. Email address: wangbin@amss.ac.cn
***Postal address: Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, ON N2L3G1, Canada. Email address: wang@uwaterloo.ca
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Abstract

In this paper, we analyse the set of all possible aggregate distributions of the sum of standard uniform random variables, a simply stated yet challenging problem in the literature of distributions with given margins. Our main results are obtained for two distinct cases. In the case of dimension two, we obtain four partial characterization results. For dimension greater than or equal to three, we obtain a full characterization of the set of aggregate distributions, which is the first complete characterization result of this type in the literature for any choice of continuous marginal distributions.

Keywords

Uniform distributionaggregationdependence uncertaintyjoint mixability

MSC classification

Primary: 60E15: Inequalities; stochastic orderings
Secondary: 62P05: Applications to actuarial sciences and financial mathematics
Type
Research Papers
Information
Journal of Applied Probability , Volume 56 , Issue 3 , September 2019 , pp. 918 - 936
Copyright
© Applied Probability Trust 2019 

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