The accurate estimation of the design Precipitation is one of the requirements for the construction of hydraulic structures, which is done by various methods of frequency analysis. Classical methods of fitting observational data use the assumption of constant parameters of distribution functions; while, many studies have been done on non-stationary data due to factors such as climate change. Therefore, this paper aims to use the functions of non-stationary parameters - if necessary - and compare them with the stationary assumption of the maximum daily precipitation data of the Atrak river basin. Mann-Kendall test and White test were used to check the non-stationary in the mean and variance of annual data. The Generalized extreme value distribution function was also fitted to the data time series. Among the 24 stations with long-term data, 5 stations with trends and 6 stations with variance non-stationary were detected. Evaluation criteria including Akaike (AIC), Bayesian (BIC), Root mean square error (RMSE), and Nash-Sutcliffe efficiency (NSE) coefficient was determined under stationary and non-stationary assumptions, for all stations. The results showed that in all stations with non-stationary, considering the mentioned conditions in the analytical calculations is a good choice. Also, the lower (5%), median (50%), and upper (95%) limit values with the return period of 100 years with both assumptions were determined and compared with the classical maximum likelihood method. The underestimation of the maximum likelihood method compared to the Bayesian method used by using Markov chain Monte Carlo (MCMC) in parameter estimation was observed. Also, Akaike criterion provided better results among the used evaluation criteria.