Probable Maximum Precipitation (PMP) is used for estimating Probable Maximum Flood (PMF) which, in turn, is used for design of major hydraulic structures, such as dams and spillways, flood protection works, and nuclear power plants. One of the commonly used methods for estimating PMP is the statistical method, also called Hershfield method that entails computation of frequency factor, adjustment of the frequency factor, construction of an enveloping curve of the frequency factor, estimation of PMP, choosing a probability distribution of PMP, and determination of the return period of PMP. There are, however, uncertainties associated with the PMP values estimated using the statistical method. This study determined the PMP values for different durations using the statistical method with data from the Brazos River basin, Texas. It was found that significant uncertainty in the PMP estimates can occur with the use of enveloping curve of the frequency factor and the number of stations involved in its construction. Hershfield's curve yielded higher frequency factor values by 16% for 1 hour duration, by 17.9% for 6 hour duration, and by 22.1% for 24 hour duration. In comparison with basin-specific values, the PMP values from the Hershfield enveloping curve were 16.8% higher for 1-hour duration, 18.5% for 6-hour duration, and 23.4% for 24-hour duration. For most of the Brazos River basin the return period of the PMP values was in the range of 1000 to 3000 years which was less than the range of 103 to 106 years reported in HMR 51, showing the degree of risk associated with the PMP values. Therefore, a basin specific-enveloping curve is suggested. From 24 commonly used statistical distributions and 5 goodness of fit tests, the Burr Type XII distribution was found to be the best frequency distribution for describing PMP. It was observed that the return period obtained from the Burr type XII frequency distribution was not significantly higher than that obtained from the hydreometeorological reports (HMRs) of National Weather Service and other studies. .