Reliability Modeling: Linear Combination and Ratio of Exponential and Rayleigh

The distributions of linear combinations, and ratios of random variables arise explicitly in many reliability problems. This has increased the need to have available the widest possible range of statistical results on products of random variables. In this paper, the exact distributions of alphaX+betaY, and X/Y are derived when X, and Y follow two of the most applied models in reliability. Computer programs for calculating the associated percentage points are also given