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Table 1 summarizes the goodness-of-fit (in terms of mean RMSE) of nonparametric and parametric distributions for the case study, varying the hydrological variable, the time scale, and the sample size. For the sake of simplicity, only the two extreme sample sizes (30 and 180 years) are reported. The fitting was performed for each calendar month, therefore Table 1 shows average RMSE results.

Table 1

Average RMSE of different probability distributions for different hydrological variables, time scales and for sample sizes of 30 and 180 years (in brackets)

Time scale k (months)
Hydrological variableDistribution13612
Precipitation (SPI) Nonparametric (Gaussian kernel) 6.1 (3.6) 10.3 (6.5) 14.9 (9.6) 20.7 (13.6) 
gamma 9.1 (5.8) 18.1 (7.6) 20.4 (11.9) 29.9 (13.2) 
Pearson type III 8.2 (3.8) 15.1 (6.9) 18.5 (11.0) 24.6 (13.1) 
Climatic balance (SPEI) Nonparametric (Gaussian kernel) 6.4 (3.7) 10.7 (6.7) 14.9 (9.7) 21.5 (13.9) 
GLO 8.4 (6.8) 15.4 (9.9) 18.4 (14.7) 28.3 (17.4) 
GEV 8.1 (4.0) 14.6 (7.1) 18.4 (12.0) 27.4 (14.4) 
Time scale k (months)
Hydrological variableDistribution13612
Precipitation (SPI) Nonparametric (Gaussian kernel) 6.1 (3.6) 10.3 (6.5) 14.9 (9.6) 20.7 (13.6) 
gamma 9.1 (5.8) 18.1 (7.6) 20.4 (11.9) 29.9 (13.2) 
Pearson type III 8.2 (3.8) 15.1 (6.9) 18.5 (11.0) 24.6 (13.1) 
Climatic balance (SPEI) Nonparametric (Gaussian kernel) 6.4 (3.7) 10.7 (6.7) 14.9 (9.7) 21.5 (13.9) 
GLO 8.4 (6.8) 15.4 (9.9) 18.4 (14.7) 28.3 (17.4) 
GEV 8.1 (4.0) 14.6 (7.1) 18.4 (12.0) 27.4 (14.4) 

Bold values indicate the best performing distribution for each combination of variable and time scale. Weather data (1950–2010) of the Terni station.

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