We present a measurement of the muon charge asymmetry from the decay of the $W$ boson via $W\ensuremath{\rightarrow}\ensuremath{\mu}\ensuremath{\nu}$ using $7.3\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ of integrated luminosity collected with the D0 detector at the Fermilab Tevatron Collider at $\sqrt{s}=1.96\text{ }\text{ }\mathrm{TeV}$. The muon charge asymmetry is presented in two kinematic regions in muon transverse momentum and event missing transverse energy: (${p}_{T}^{\ensuremath{\mu}}>25\text{ }\text{ }\mathrm{GeV}$, ${\mathrm{E\ensuremath{\llap{\not\;}}}}_{T}>25\text{ }\text{ }\mathrm{GeV}$) and (${p}_{T}^{\ensuremath{\mu}}>35\text{ }\text{ }\mathrm{GeV}$, ${\mathrm{E\ensuremath{\llap{\not\;}}}}_{T}>35\text{ }\text{ }\mathrm{GeV}$). The measured asymmetries are compared with theory predictions made using three parton distribution function sets. The data at ${p}_{T}^{\ensuremath{\mu}}>35\text{ }\text{ }\mathrm{GeV}$, ${\mathrm{E\ensuremath{\llap{\not\;}}}}_{T}>35\text{ }\text{ }\mathrm{GeV}$, and larger values of $|{\ensuremath{\eta}}^{\ensuremath{\mu}}|$ favor an increased $d(x)/u(x)$ ratio at higher values of $x$ than is predicted.