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

David M. Bradley·Ramesh C. Gupta
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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.

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David M. Bradley, Ramesh C. Gupta. 2004-11-12. On the Distribution of the Sum of n Non-Identically Distributed Uniform Random Variables. https://doi.org/10.1023/a%3A1022483715767

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