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Given an Orlicz function $M$, we show which random variables $\xi_i$,$i=1,...,n$ generate the associated Orlicz norm, i.e., which random variablesyield $\mathbb{E} \max\limits_{1\leq i \leq n}|x_i\xi_i| \sim\norm{(x_i)_{i=1}^n}_M$. As a corollary we obtain a representation for thedistribution function in terms of $M$ and $M'$ which can be easily applied tomany examples of interest.

An Inversion Formula for Orlicz Norms and Sequences of Random Variables