Geodesic
Linear combination, product and ratio of normal and logistic random variables
Kybernetika, Tome 41 (2005) no. 6, p. [787]

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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.
Classification : 60E05, 62E10, 62E15, 62P30
Keywords: linear combination of random variables; logistic distribution; normal distribution; products of random variables; ratios of random variables 
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     author = {Nadarajah, Saralees},
     title = {Linear combination, product and ratio of normal and logistic random variables},
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     zbl = {1243.62020},
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Nadarajah, Saralees. Linear combination, product and ratio of normal and logistic random variables. Kybernetika, Tome 41 (2005) no. 6, p. [787]. http://geodesic.mathdoc.fr/item/KYB_2005__41_6_a7/