Annals of the Institute of Statistical Mathematics

, Volume 54, Issue 3, pp 689–700

On the Distribution of the Sum of n Non-Identically Distributed Uniform Random Variables

  • David M. Bradley
  • Ramesh C. Gupta
Article

DOI: 10.1023/A:1022483715767

Cite this article as:
Bradley, D.M. & Gupta, R.C. Annals of the Institute of Statistical Mathematics (2002) 54: 689. doi:10.1023/A:1022483715767
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Abstract

The distribution of the sum of independent identically distributed uniform random variables is well-known. However, it is sometimes necessary to analyze data which have been drawn from different uniform distributions. By inverting the characteristic function, we derive explicit formulae for the distribution of the sum of n non-identically distributed uniform random variables in both the continuous and the discrete case. The results, though involved, have a certain elegance. As examples, we derive from our general formulae some special cases which have appeared in the literature.

Uniform distribution probability density convolution Fourier transform sine integrals 

Copyright information

© The Institute of Statistical Mathematics 2002

Authors and Affiliations

  • David M. Bradley
    • 1
  • Ramesh C. Gupta
    • 2
  1. 1.Department of Mathematics and StatisticsUniversity of Maine, OronoU.S.A.
  2. 2.Department of Mathematics and StatisticsUniversity of Maine, OronoU.S.A.

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