In this note we consider an alternative approach to compute the distribution of the sum of independent exponential random variables. In particular, by considering the logarithmic relation between exponential and beta distribution functions and by considering the Wilks’ integral representation for the product of independent beta random variables, we provide a closed-form expression for the distribution of the sum of independent exponential random variables. The expression we obtain is simpler than the ones previously obtained in the literature.
On the distribution of sums of independent exponential random variables via Wilks' integral representation
FAVARO, STEFANO;
2010-01-01
Abstract
In this note we consider an alternative approach to compute the distribution of the sum of independent exponential random variables. In particular, by considering the logarithmic relation between exponential and beta distribution functions and by considering the Wilks’ integral representation for the product of independent beta random variables, we provide a closed-form expression for the distribution of the sum of independent exponential random variables. The expression we obtain is simpler than the ones previously obtained in the literature.
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