AISM 54, 689-700

© 2002 ISM

## On the distribution of the sum of *n* non-identically distributed uniform random variables

### David M. Bradley and Ramesh C. Gupta

Department of Mathematics and Statistics, University of Maine, Orono, ME 04469-5752, U.S.A., e-mail: dbradley@e-math.ams.org; rcgupta@maine.maine.edu

(Received August 28, 2000)

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.

Key words and phrases:
Uniform distribution, probability density, convolution, Fourier transform, sine integrals.

**Source**
(TeX , DVI )