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Linear combination, product and ratio of normal and logistic random variables. (English) Zbl 1243.62020
Summary: The distributions of linear combinations, products and ratios of random variables arise in many areas of engineering. In this note, the exact distributions of $$\alpha X+\beta Y$$, $$| XY |$$ and $$| X/Y |$$ 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.

##### MSC:
 62E15 Exact distribution theory in statistics 62P30 Applications of statistics in engineering and industry; control charts
##### Keywords:
logistic distribution; product; ratio
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