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Table 3 The best univariate distribution and copula function that has been selected based on the comparison of chi-squared and RMSE values between theoretical and empirical cumulative probabilities. Ave. Sev., average severity; l, location; s, scale; ml, meanlog; sl, sdlog; sh, shape; r, rate; m, mean; sd, standard deviation; P, parameter

From: Climate change impact assessment on mild and extreme drought events using copulas over Ankara, Turkey

Time period Dataset Univariate Bivariate
Distribution Parameter Chi-squared Copula (P) RMSE
Reference Duration Logistic l = 17.372; s = 4.671 0.295 Normal (0.47) 0.031
Ave. Sev. Logistic l = 0.886; s = 0.114 0.373
HadGEM 4.5 Duration Lognormal ml = 2.881; sl = 0.669 0.165 Frank (1.93) 0.036
Ave. Sev. Logistic l = 0.799; s = 0.14 0.195
HadGEM 8.5 Duration Logistic l = 15.326; s = 3.156 0.076 Frank (0.18) 0.039
Ave. Sev. Gamma sh = 9.429; r = 10.642 0.056
MPI 4.5 Duration Gamma sh = 3.385; r = 0.193 0.087 Frank (2.95) 0.024
Ave. Sev. Gamma sh = 8.878; r = 9.825 0.127
MPI 8.5 Duration Normal mean = 15.935; sd = 7.23 0.338 Frank (0.15) 0.03
Ave. Sev. Logistic l = 0.918; s = 0.168 0.152
GFDL 4.5 Duration Gamma sh = 5.633; rate = 0.288 0.184 Frank (2.93) 0.031
Ave. Sev. Lognormal ml = −0.115; sl = 0.271 0.065
GFDL 8.5 Duration Gamma sh = 3.459; r = 0.217 0.074 Normal (0.47) 0.032
Ave. Sev. Lognormal ml = −0.152; sl = 0.292 0.123