Distributions of depth of shower maximum ($X_\mathrm{max}$) are parametrized and results are compared to previous studies. Large samples of extensive air showers were simulated using the CONEX simulation package in the energy range 10$^{17-20}$ eV for four primary masses: proton, carbon silicon and iron. Three functions are studied to parametrize the distributions of $X_\mathrm{max}$: exponentially modified Gaussian (EMG), generalized Gumbel (GMB) and log-normal (LOG). Results allow for a direct comparison between the proposed functional forms in terms of the Akaike information theory and this comparison suggests that GMB function should be used in the description of $X_\mathrm{max}$ data. LOG distribution also provides reasonable fits for low-mass primaries while the EMG function should be discarded. A parametrization of each function for each used hadronic interaction model is discussed and a comparison to previous parametrizations is presented.