AISM 54, 689-700
© 2002 ISM
(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.
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