<p>Probable Maximum Precipitation (PMP) is essential for estimating Probable Maximum Flood, a key factor in designing major hydraulic structures. While the Hershfield method is widely used for PMP estimation, its frequency factor (k_m) can exhibit positive or negative biases, depending on the region, and its nomographs require updates for broader applicability. Additionally, small sample sizes introduce uncertainty in PMP estimates. This study evaluated PMP values for 24-h annual maximum precipitation using the newly developed Spectral PMP method, the Hershfield method as the standard reference, and the Own PMP method as a basin-specific approach. The Spectral PMP method refined k_m through uncertainty and risk analysis, utilizing the coefficient of variation and frequency analysis of basin-specific data from the Nehbandan synoptic station in Iran’s Shour River basin and seven rain-gauge stations in East Texas, USA. Results showed that the Spectral method estimated PMP with a negative bias relative to Hershfield’s approach, with the standard uncertainty range of 3–23.4% in Nehbandan and − 14 to 54% in East Texas, indicating Hershfield's tendency toward positive bias in both regions. Additionally, Hershfield’s k_m was found to be sensitive to outliers and standard deviation but not to long-term trends, causing upper-limit biases in seven of the eight stations studied. Conversely, the Spectral PMP method exhibited reasonable sensitivity to the data series' characteristics, offering a more adaptable approach to PMP estimation.</p>