ON THE CONVOLUTION OF EXPONENTIAL DISTRIBUTIONS

Abstract

The distribution of the sum of n independent random variables having exponential distributions with different parameters βi (i = 1, 2, ..., n) is given in [2], [3], [4] and [6]. In [1], by using Laplace transform, Jasiulewicz and Kordecki generalized the results obtained by Sen and Balakrishnan in [6] and established a formula for the distribution of this sum without conditions on the parameters βi. The aim of this note is to present a method to find the distribution of the sum of n independent exponentially distributed random variables with different parameters. Our method can also be used to handle the case when all βi are the same.

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