Estimation of probable maximum flood discharges with certain return periods is essential for the design of hydraulic structures. The peak value of a flood having a pre-defined average return period is determined by frequency analysis. The longer the period of the observed flood peaks series, the more realistic the results of the flood frequency analysis, because the parameters of the probability distribution functions estimated from longer sample series tend to be close to their population values. Parameters of four commonly used probability distribution functions with recorded series of annual flood peaks at ten stream-gauging stations in the Ceyhan River Basin in southern Turkey were computed by the methods of Probability-Weighted Moments and Maximum-Likelihood. The plotting position formulas of Landwehr, Hosking, Cunnane, and Weibull were used separately for estimating the non-exceedence probabilities of sample events in computing the distribution parameters by the Probability-Weighted Moments method. Log-Pearson-3, Log-Normal-3, Generalized Extreme Value, and Wakeby distribution functions were applied to the observed annual maximum flood peaks series of the ten stream-gauging stations to determine the frequency relationship of the peak flood discharges vs return periods. The performances of four different PWM methods and the Maximum-Likelihood method were evaluated by Kolmogorov-Simirnov, Cramer von Misses, and Chi-Square goodness-of-fit (GOF) tests. The frequency relationships given by the PWM method using either one of Landwehr, Hosking, and Cunnane plotting position formulas were close to each other, whereas the Weibull plotting position formula produced appreciably under-estimating quantiles than the other methods. As the Wakeby distribution was observed to be successful in overall performance of three goodness-of-fit tests, the Log-Normal-3 distribution by the method of Maximum-Likelihood was one of the most successful distributions. However, the method of Maximum-Likelihood was not so successful with Log-Pearson-3 and Generalized Extreme Value distributions.