For a continuous Young function \(\phi\) and homeomorphism h between the unit interval \(I=[0,1]\) and the extended real line \(\bar R,\) define a metric \(d_{h,\phi}\) on distribution functions f, G by \(d_{h,\phi}(F,G)=\| F\circ h-G\circ h\|_{\phi}\), where \(\| \cdot \|_{\phi}\) denotes the Orlicz norm on the space \(L^{\phi}=L^{\phi}(I,B(I),\lambda)\) where \(\lambda\) is the Lebesgue measure. It is shown that every such metric metrizes the topology of weak convergence on distribution functions.