Geodesic
Linear combination, product and ratio of normal and logistic random variables
Kybernetika, Tome 41 (2005) no. 6, pp. 787-798

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The distributions of linear combinations, products and ratios of random variables arise in many areas of engineering. In this note, the exact distributions of $\alpha X + \beta Y$, $\vert X Y \vert $ and $\vert X/Y \vert $ are derived when $X$ and $Y$ are independent normal and logistic random variables. The normal and logistic distributions have been two of the most popular models for measurement errors in engineering.
The distributions of linear combinations, products and ratios of random variables arise in many areas of engineering. In this note, the exact distributions of $\alpha X + \beta Y$, $\vert X Y \vert $ and $\vert X/Y \vert $ are derived when $X$ and $Y$ are independent normal and logistic random variables. The normal and logistic distributions have been two of the most popular models for measurement errors in engineering.
Classification : 60E05, 62E10, 62E15, 62P30
Keywords: linear combination of random variables; logistic distribution; normal distribution; products of random variables; ratios of random variables 
Nadarajah, Saralees. Linear combination, product and ratio of normal and logistic random variables. Kybernetika, Tome 41 (2005) no. 6, pp. 787-798. http://geodesic.mathdoc.fr/item/KYB_2005_41_6_a7/
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     title = {Linear combination, product and ratio of normal and logistic random variables},
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[2] Prudnikov A. P., Brychkov Y. A., Marichev O. I.: Integrals and Series (Volumes 1, 2 and 3). Gordon and Breach Science Publishers, Amsterdam 1986