Spatiotemporal normality analysis of streamflow time series is essential in flood controlling, hydrological modeling, and water resources management. This study aims to investigate spatiotemporal analysis of streamflow normality and determine suitable probability distribution using theory driven, descriptive statistics, graphical, and IDW (Inverse Distance Weighted) interpolation methods in Western and Northwestern Iran over a 51-year period (1961–2011). The results of theory-driven methods indicated that on average 76.85% of the streamflow time series did not follow the normal distribution at 0.05 significance level. Moreover, the results exhibited that monthly time series had the highest variability, especially in summer and autumn months, and those did follow the normal distribution in a lower rate than annual time series. Although the normality analysis methods have different sensitivities to various changes in the data series and their outputs sometime have discrepancies, the SW (Shapiro–Wilk) test is recommended for normality analysis in the hydrological time series. The results determined that the GEV (Generalized Extreme Value) distribution had the highest best fit distribution for the streamflow time series (49.62%) while the Pearson Type III (1.15%) had the lowest best fit distribution. Furthermore, the highest numbers of suitable time series for GEV were in the winter months while the lowest numbers of those series were in the summer months. The study area is specified by high variability in magnitude of precipitation, followed by the streamflow variability in monthly and seasonal regimes. In the semi-arid regions, variability of streamflow time series driven by precipitation variability or anthropogenic changes is significant and mostly responds to variation in precipitation. The findings indicated that it is difficult to determine a dominant distribution to fit all monthly and annual streamflow time series in a semi-arid region such as Iran

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