The stationary probabilities of different modulation and coding schemes (MCS) are required for dimensioning an OFDMA based network. In this paper, we introduce a semi-analytical approach to find out these stationary probabilities for a WiMAX network in downlink (DL) with users served by the best base station (BS). Using Monte Carlo simulations, we find the spatial distributions of effective signal to interference-plus-noise ratio ($SINR_{eff}$) for different values of shadowing standard deviation ($\sigma_{SH}$). With the help of distribution fit, we show that generalized extreme value (GEV) distribution provides a good fit for different frequency reuse schemes. Furthermore, by applying curve fitting, we demonstrate that the parameters of GEV distributions, as a function of $\sigma_{SH}$ values, can be expressed using polynomials. These polynomial can then be used off-line (in place of time consuming simulations) to find out GEV cumulative distribution function (CDF), and hence the stationary probabilities of MCS, for any desired value of $\sigma_{SH}$. We further show that these polynomials can be used for other cell configurations with acceptable deviation and significant time saving.