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Kybernetika 41(6):787-798, 2005.

Linear Combination, Product and Ratio of Normal and Logistic Random Variables

Saralees Nadarajah


Abstract:

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.


Keywords: linear combination of random variables; logistic distribution; normal distribution; products of random variables; ratios of random variables;


AMS: 62E15;


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BIB TeX

@article{kyb:2005:6:787-798,

author = {Nadarajah, Saralees},

title = {Linear Combination, Product and Ratio of Normal and Logistic Random Variables},

journal = {Kybernetika},

volume = {41},

year = {2005},

number = {6},

pages = {787-798}

publisher = {{\'U}TIA, AV {\v C}R, Prague },

}


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