Hydrological time series frequently exhibit periodic trends with variables such as rainfall, runoff, and evaporation rates often following annual cycles. Seasonal variations further contribute to the complexity of these data sets. A critical aspect of analyzing such phenomena is estimating realistic return intervals, making the precise determination of these values essential. Given this importance, selecting an appropriate probability distribution is paramount. To address this need, we introduce a flexible probability model specifically designed to capture periodicity in hydrological data. We thoroughly examine its fundamental mathematical and statistical properties, including the asymptotic behavior of the probability density function (PDF) and hazard rate function (HRF), to enhance predictive accuracy. Our analysis reveals that the PDF exhibits polynomial decay as (Formula presented.), ensuring heavy-tailed behavior suitable for extreme events. The HRF demonstrates decreasing or non-monotonic trends, reflecting variable failure risks over time. Additionally, we conduct a simulation study to evaluate the performance of the estimation method. Based on these results, we refine return period estimates, providing more reliable and robust hydrological assessments. This approach ensures that the model not only fits observed data but also captures the underlying dynamics of hydrological extremes.
