Abstract. In this study, 25 years mean monthly out flow discharge data of Farakka barrage was used (i.e., from 1949 to 1968). Farakka barrage is located between on Ganga River. Spatial and temporal variation in flow rate for any particular area is very common due to various meteorological and other factors existing in nature. But large variations in these factors cause extreme events (e. g., floods and droughts). Monthly outflow discharge for a particular critical month are predicted using statistical models (ARMA Model and Copula Model). Different Copulas (i.e., Normal, t, Frank, Clayton, Gumbel–Hoggard, Ali–Mikhail–Haq) are used for this purpose and the copula model is selected based on distribution functions (Normal distribution, Lognormal distribution, Extreme value type-1 distribution, Generalized Extreme value type, Gamma distribution, Weibull distribution, Exponential distribution). The distribution is selected based on the Mean square error (MSE), Akaike Information Criterion (AIC), and Bayesian Information Criterion (BIC). The model parameters were computed using the Maximum Likelihood (ML) estimation method.