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doi:10.1016/j.csda.2005.07.022 
Copyright © 2005 Elsevier B.V. All rights reserved.
The distribution of sums, products and ratios for Lawrance and Lewis's bivariate exponential random variables
Received 16 February 2005;
revised 27 July 2005;
accepted 28 July 2005.
Available online 22 August 2005.
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Abstract
We derive the exact distributions of R=X+Y, P=XY and W=X/(X+Y) and the corresponding moment properties when X and Y follow Lawrence and Lewis's bivariate exponential distribution. The expressions turn out to involve special functions. We also provide extensive tabulations of the percentage points associated with the distributions. These tables—obtained using intensive computing power—will be of use to practitioners of the bivariate exponential distribution.
Keywords: Lawrance and Lewis's bivariate exponential distribution; Sums of random variables; Product of random variables; Ratios of random variables
