Table 3 : Estimated biases and MSEs of estimators computed using five copulas.
n | Pa | Bias | MSE | |||||||||
Fr | Cl | Gu | Jo | No | Fr | Cl | Gu | Jo | No | |||
15 | 0.3 | 0.68 | 0.17 | -0.04 | 1.32 | 0.86 | 29.67 | 19.19 | 8.64 | 9.00 | 11.85 | |
0.45 | 0.49 | 0.73 | 0.72 | 0.43 | 35.30 | 9.69 | 9.35 | 8.97 | 9.97 | |||
0.45 | 0.78 | 0.40 | 0.67 | 0.22 | 42.66 | 22.00 | 27.28 | 19.74 | 22.90 | |||
0.89 | 0.80 | 0.91 | 0.90 | 0.93 | 29.84 | 19.66 | 16.60 | 7.73 | 26.25 | |||
0.61 | 0.22 | 0.55 | 0.15 | 0.02 | 5.91 | 0.88 | 0.54 | 0.21 | 0.08 | |||
0.6 | 0.62 | 0.65 | 0.09 | 0.98 | 1.70 | 36.69 | 39.82 | 22.67 | 34.55 | 23.82 | ||
0.82 | 0.45 | 2.10 | 1.46 | 2.01 | 35.54 | 30.53 | 31.65 | 33.90 | 33.20 | |||
0.65 | -0.17 | -1.09 | 0.74 | 1.15 | 50.23 | 58.20 | 41.20 | 62.01 | 38.78 | |||
0.90 | 1.95 | 0.92 | 1.89 | 2.63 | 31.51 | 29.29 | 34.01 | 24.87 | 37.02 | |||
0.45 | 0.23 | 0.24 | 0.77 | -0.01 | 8.77 | 1.50 | 0.62 | 4.38 | 0.01 | |||
0.9 | 0.78 | -0.39 | 0.60 | 0.03 | 0.40 | 8.82 | 42.09 | 38.29 | 34.40 | 2.53 | ||
0.89 | 0.44 | 3.84 | 0.50 | 0.50 | 4.41 | 68.48 | 44.15 | 37.43 | 4.07 | |||
0.18 | -1.34 | -0.39 | 0.19 | -0.04 | 15.69 | 32.81 | 61.35 | 49.92 | 4.21 | |||
0.85 | 0.97 | 4.56 | 1.09 | 0.10 | 5.58 | 36.47 | 41.02 | 37.41 | 4.02 | |||
0.07 | 0.42 | 0.16 | 0.42 | 0.00 | 19.92 | 61.66 | 11.95 | 89.07 | 3.67 | |||
30 | 0.3 | 0.01 | -0.01 | -0.35 | 0.01 | 0.11 | 13.50 | 14.29 | 17.15 | 7.49 | 14.17 | |
-0.85 | -0.91 | -1.11 | -1.40 | -0.81 | 7.50 | 8.30 | 8.08 | 9.30 | 7.46 | |||
-0.03 | 0.03 | 0.83 | -0.35 | -0.08 | 21.83 | 24.21 | 18.98 | 27.19 | 21.70 | |||
-1.15 | -1.10 | -2.06 | -1.54 | -1.32 | 12.67 | 11.89 | 12.58 | 11.10 | 12.61 | |||
0.14 | 0.05 | 0.05 | 0.01 | -0.01 | 1.70 | 0.20 | 0.06 | 0.11 | 0.02 | |||
0.6 | -0.03 | 0.11 | -0.05 | -0.02 | -0.19 | 12.43 | 15.16 | 13.75 | 14.30 | 14.18 | ||
-0.96 | -0.95 | -0.85 | -1.11 | -1.79 | 8.32 | 6.93 | 7.93 | 6.24 | 7.72 | |||
-0.96 | -0.95 | -0.85 | -1.11 | -1.79 | 8.32 | 6.93 | 7.93 | 6.24 | 7.72 | |||
-1.14 | -1.18 | -1.54 | -1.48 | -1.04 | 13.05 | 10.59 | 11.73 | 11.24 | 11.49 | |||
0.27 | 0.20 | 0.08 | 0.15 | -0.01 | 3.97 | 1.11 | 0.28 | 0.99 | 0.01 | |||
0.9 | 0.78 | -0.94 | 0.61 | 0.03 | 0.41 | 8.83 | 42.09 | 38.29 | 34.40 | 2.53 | ||
0.88 | 0.44 | 3.84 | 0.50 | 0.50 | 4.42 | 68.48 | 44.15 | 37.44 | 4.08 | |||
0.18 | -1.34 | -0.39 | 0.19 | -2.04 | 15.70 | 32.81 | 61.35 | 49.92 | 4.21 | |||
0.85 | 0.97 | 4.56 | 1.09 | 0.11 | 5.58 | 36.47 | 41.02 | 37.41 | 4.02 | |||
0.07 | 0.43 | 0.16 | 0.43 | 0.01 | 19.92 | 61.66 | 11.95 | 89.07 | 3.61 | |||
50 | 0.3 | 0.1 | 0.01 | -0.33 | -0.07 | 0.13 | 8.94 | 9.13 | 6.22 | 8.65 | 8.46 | |
-0.61 | -0.53 | -0.65 | -0.59 | -0.5 | 4.81 | 4.43 | 4.79 | 4.53 | 4.85 | |||
0.2 | -0.03 | 0.4 | -0.2 | 0.06 | 13.29 | 15.6 | 10.37 | 15.13 | 13.29 | |||
-0.63 | -0.64 | -1.12 | -0.66 | -0.68 | 7.77 | 7.98 | 8.31 | 7.28 | 7.59 | |||
0.07 | 0.05 | 0.03 | 0.05 | -0.01 | 1.05 | 0.11 | 0.02 | 0.1 | 0.01 | |||
0.6 | 0.07 | 0.15 | -0.19 | -0.09 | -0.26 | 8.21 | 9.67 | 8.56 | 9.29 | 8.68 | ||
-0.06 | -0.52 | -0.65 | -0.57 | -0.45 | 4.64 | 4 | 4.73 | 4.61 | 4.46 | |||
-0.06 | 0.15 | -0.33 | 0.06 | 0.03 | 12.98 | 15.56 | 14.18 | 13.83 | 15.36 | |||
-0.76 | -0.67 | -0.75 | -0.82 | -0.47 | 7.42 | 6.95 | 6.05 | 6.89 | 7.23 | |||
0.16 | 0.04 | 0.01 | 0.09 | -0.01 | 2.17 | 0.6 | 0.16 | 0.52 | 0.01 | |||
0.9 | -0.08 | -0.14 | -0.09 | 0.04 | 0.17 | 5.35 | 8.32 | 9.28 | 8.96 | 9.49 | ||
-0.41 | -0.54 | -0.54 | -0.68 | -0.6 | 3.61 | 3.94 | 4.93 | 4.02 | 4.53 | |||
-0.1 | -0.24 | -0.16 | 0.02 | 0.14 | 8.78 | 13.27 | 14.88 | 14.72 | 1.52 | |||
-0.56 | -0.72 | -0.68 | -0.85 | -0.72 | 5.97 | 6.48 | 7.83 | 6.42 | 7.59 | |||
1.29 | 0.52 | 0.21 | 0.6 | -0.01 | 34.51 | 13.39 | 2.98 | 14.57 | 0.52 | |||
100 | 0.3 | -0.01 | -0.04 | -0.01 | 5.84 | 6.16 | 6.02 | 5.64 | 5.39 | 5.84 | 6.16 | |
-0.28 | -0.39 | -0.23 | 2.95 | 3.05 | 2.87 | 2.8 | 2.77 | 2.95 | 3.05 | |||
-0.04 | -0.02 | 0.01 | 6.94 | 7.35 | 7.17 | 7.22 | 7.57 | 6.94 | 7.34 | |||
-0.37 | -0.37 | -0.26 | 3.62 | 3.07 | 3.76 | 3.62 | 3.43 | 3.62 | 3.07 | |||
-0.01 | 0.01 | 0.01 | 0.02 | 0.01 | 0.42 | 0.05 | 0.02 | 0.05 | 0.01 | |||
0.6 | -0.01 | -0.04 | 0.12 | 0.11 | 0.01 | 4.79 | 5.46 | 5.95 | 5.79 | 5.45 | ||
-0.3 | -0.3 | -0.24 | -0.22 | -0.38 | 2.85 | 2.54 | 3.01 | 2.5 | 2.97 | |||
-0.05 | -0.11 | 0.18 | 0.12 | 0.02 | 6.16 | 7.34 | 7.24 | 7.34 | 6.13 | |||
-0.31 | -0.31 | -0.29 | -0.33 | -0.28 | 3.67 | 2.93 | 3.41 | 3.11 | 2.69 | |||
0.06 | 0.05 | 0.04 | 0.07 | -0.01 | 0.99 | 0.27 | 0.07 | 0.27 | 0.01 | |||
0.9 | 0.01 | -0.13 | -0.15 | 0.13 | 0.1 | 3.61 | 5.44 | 5.58 | 5.95 | 2.34 | ||
-0.24 | -0.39 | -0.31 | -0.28 | -0.39 | 2.08 | 2.24 | 3.03 | 2.22 | 1.11 | |||
0.01 | -0.15 | -0.18 | 0.14 | 0.12 | 4.46 | 6.81 | 7.02 | 7.45 | 5.71 | |||
-0.27 | -0.42 | -0.37 | -0.31 | -0.43 | 2.65 | 2.77 | 1.75 | 2.75 | 3.79 | |||
0.72 | 0.33 | 0.1 | 0.37 | -0.01 | 13.66 | 6.52 | 1.39 | 6.87 | 0.95 | |||
500 | 0.3 | -0.01 | 0.07 | -0.06 | 0.01 | -0.03 | 1.04 | 1.08 | 1.08 | 0.96 | 1.09 | |
0.01 | -0.06 | -0.04 | -0.06 | -0.12 | 0.53 | 0.57 | 0.47 | 0.51 | 0.47 | |||
-0.09 | 0.04 | -0.07 | -0.05 | 0.04 | 1.28 | 1.35 | 1.31 | 1.2 | 1.28 | |||
-0.08 | -0.11 | -0.04 | -0.08 | -0.09 | 0.64 | 0.55 | 0.6 | 0.62 | 0.48 | |||
0.01 | 0.01 | 0.01 | 0.05 | -0.01 | 0.08 | 0.08 | 0.03 | 0.09 | 0.01 | |||
0.6 | 0.01 | 0.13 | 0.01 | 0.08 | 0.01 | 0.8 | 1.02 | 1.09 | 0.96 | 0.08 | ||
-0.11 | -0.12 | -0.09 | -0.11 | -0.06 | 0.53 | 0.49 | 0.49 | 0.34 | 0.53 | |||
0.03 | 0.08 | 0.01 | 0.1 | 0.01 | 1.09 | 1.2 | 1.38 | 1.27 | 1.19 | |||
-0.1 | -0.13 | -0.1 | -0.12 | -0.07 | 0.56 | 0.63 | 0.56 | 0.61 | 0.67 | |||
-0.01 | -0.01 | 0.01 | 0.02 | 0.01 | 0.19 | 0.05 | 0.01 | 0.05 | 0.01 | |||
0.9 | -0.01 | -0.09 | 0.07 | -0.09 | 0.04 | 0.58 | 0.94 | 1.04 | 1.12 | 0.87 | ||
-0.07 | -0.07 | -0.08 | -0.08 | -0.09 | 0.4 | 0.36 | 0.48 | 0.39 | 0.29 | |||
-0.01 | -0.08 | -0.17 | -0.09 | 0.05 | 0.68 | 1.15 | 1.34 | 1.36 | 0.11 | |||
-0.08 | -0.09 | -0.08 | -0.09 | -0.1 | 0.47 | 0.43 | 0.59 | 0.48 | 0.4 | |||
0.18 | 0.14 | 0.01 | 0.06 | -0.01 | 2.31 | 1.21 | 0.25 | 1.2 | 0.01 | |||
(Pa, Fr, Cl, Gu, Jo and No are Parameter, Frank, Clayton, Gumbel, Joe and Normal respectively).