2004/11/12 by David M. Bradley, Ramesh C. Gupta · 1 citation
Mathematics · #math.ST #stat.TH
paper · pdf · doi:10.1023/a:1022483715767
published as Annals of the Institute of Statistical Mathematics, Vol. 54, (2002), no. 3, pp. 689--700. MR 1932412 (2003h:60029) · 20 pages
arxiv created 2004/11/12 · arxiv updated 2010/05/25
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.