ON THE CONVOLUTION OF EXPONENTIAL DISTRIBUTIONS

The distribution of the sum of n independent random variables having exponential distributions with di？？erent parameters ¯i (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 param- eters ¯i: The aim of this note is to present a method to ¯nd the distribution of the sum of n independent exponentially distributed random variables with di？？erent parameters. Our method can also be used to handle the case when all ¯i are the same.