Lifetime of excited electronic states inside the 4f configuration of rare-earth elements embedded in chalcogenide glasses is very sensitive to medium-range structural changes of the host glasses. We have measured lifetimes of the 1.6$mu extrm{m}$ emission originating from Pr$^$3+/ : ($^3$F$_3$, $^3$F$_4$)longrightarrow$^3$H$_4$ transition in amorphous chalcogenide samples consisting of Ge, Sb, and Se elements. The measured lifetimes fumed out to have their maximum at the mean coordination number of -2.67, which arises accordingly from structural changes of the host glasses from 2 dimensional layers to 3 dimensional networks. This new finding supports that the so-called topological structure model together with chemically ordered network model is adequate to explain relationship between the emission properties of rare-earth elements and the medium-range structures of amorphous chalcogenide hosts with a large covalent bond nature. Thus, it is validated to predict site distribution and lifetime of rare-earth elements doped in chalcogenide glasses simply based on their mean coordination number.