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

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

2004-11-12

arxiv.org/abs/math/0411298v1

Annals of the Institute of Statistical Mathematics, Vol. 54, (2002), no. 3, pp. 689--700. MR 1932412 (2003h:60029)

Mathematics

Statistics Theory

20 pages

Scientific paper

10.1023/A:1022483715767

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.

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