We have calculated the Bjorken-x dependence of the kaon and pion valence quark distributions in a statistical model. Each meson is described by a Fock state expansion in terms of quarks, antiquarks and gluons. Although Drell-Yan experiments have measured the pion valence quark distributions directly, the kaon valence quark distributions have only been deduced from the measurement of the ratio $bar{u}_K(x)/bar{u}_pi(x)$. We show that, using no free parameters, our model predicts the decrease of this ratio with increasing x.