The limit behaviour of the extreme order statistics arising from n two-dimensional independent and non-identically distributed random vectors is investigated. Necessary and sufficient conditions for the weak convergence of the distribution function (d.f.) of the vector of extremes, as well as the form of the limit d.f.'s, are obtained. Moreover, conditions for the components of the vector of extremes to be asymptotically independent are studied.

The distributions of linear combinations, products and ratios of random variables arise in many areas of engineering. In this note, the exact distributions of $\alpha X+\beta Y$, $\left|XY\right|$ 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.