###### 모의실험 pp=0.99, 즉 .99분위수에 대한 신뢰구간 ###################### ###### n = 300 # 모의실험1 GEV distribution: quantile estimation with n=300 nboot=1000 n.sim=500 p=0.99 xi NCL Normal NBPct NBBCa SBPct PBOne PBTwo 0.1 0.9 ACL NA 0.77 0.776 0.886 0.922 0.878 LENGTH NA 25.5 25.7 28.7 27.2 21.4 (NA) (0.57) (0.62) (0.39) (0.24) (0.18) SYMM2 NA 0.66 0.71 0.72 0.81 0.94 (NA) (0.05) (0.07) (0.32) (0.38) (0.35) (NA) (1.53) (1.72) (1.52) (1.47) (1.93) 0.1 0.95 ACL NA 0.79 0.934 0.932 0.972 0.93 LENGTH NA 28.6 45.4 34.9 32.8 25.6 (NA) (0.62) (1.24) (0.5) (0.3) (0.22) SYMM2 NA 0.64 1.67 0.9 0.97 1.06 (NA) (0.11) (0.9) (0.49) (0.51) (0.49) (NA) (1.38) (3.21) (1.7) (1.62) (1.97) 0.2 0.9 ACL NA 0.798 0.804 0.876 0.932 0.888 LENGTH NA 40.2 40.2 43.9 43.5 33.3 (NA) (0.97) (0.99) (0.64) (0.44) (0.31) SYMM2 NA 0.81 0.93 0.86 0.97 1.11 (NA) (0.12) (0.15) (0.33) (0.46) (0.4) (NA) (1.79) (2.07) (1.63) (1.74) (2.46) 0.2 0.95 ACL NA 0.808 0.954 0.926 0.962 0.934 LENGTH NA 44.4 76.3 53.6 52.8 39.8 (NA) (1.06) (2.21) (0.8) (0.54) (0.38) SYMM2 NA 0.75 2.11 1.06 1.14 1.24 (NA) (0.15) (0.95) (0.51) (0.62) (0.57) (NA) (1.6) (4.19) (1.83) (1.87) (2.38) 0.3 0.9 ACL NA 0.81 0.806 0.878 0.942 0.894 LENGTH NA 69.9 70.9 67.9 69.6 51.6 (NA) (2.05) (2.12) (1.17) (0.77) (0.53) SYMM2 NA 0.89 1.03 0.9 1.08 1.2 (NA) (0.15) (0.18) (0.28) (0.51) (0.39) (NA) (2.22) (2.53) (1.65) (1.88) (2.55) 0.3 0.95 ACL NA 0.818 0.946 0.924 0.976 0.934 LENGTH NA 79.7 140 83.6 85.2 61.9 (NA) (2.55) (5.74) (1.49) (0.96) (0.63) SYMM2 NA 0.86 2.33 1.13 1.26 1.36 (NA) (0.16) (1.03) (0.47) (0.68) (0.58) (NA) (2.13) (4.73) (1.92) (2.05) (2.53) 0.4 0.9 ACL NA 0.79 0.792 0.852 0.966 0.898 LENGTH NA 109 116 102 114 81.4 (NA) (3.27) (4.85) (1.94) (1.44) (0.94) SYMM2 NA 0.86 0.96 0.81 1.19 1.25 (NA) (0.1) (0.12) (0.23) (0.56) (0.44) (NA) (2.18) (2.65) (1.76) (2.34) (3.07) 0.4 0.95 ACL NA 0.816 0.93 0.932 0.982 0.94 LENGTH NA 126 255 127 140 98 (NA) (4.34) (19.46) (2.54) (1.81) (1.14) SYMM2 NA 0.86 2.44 1.03 1.46 1.47 (NA) (0.18) (0.98) (0.42) (0.82) (0.63) (NA) (2.26) (5.22) (2.11) (2.61) (3.14) 0.5 0.9 ACL NA 0.776 0.786 0.852 0.968 0.904 LENGTH NA 180 193 156 176 122 (NA) (6.46) (7.75) (3.07) (2.24) (1.45) SYMM2 NA 0.84 1.01 0.72 1.23 1.21 (NA) (0.09) (0.11) (0.2) (0.61) (0.43) (NA) (2.65) (3.1) (1.8) (2.22) (2.76) 0.5 0.95 ACL NA 0.812 0.948 0.922 0.992 0.954 LENGTH NA 203 459 195 220 147 (NA) (7.36) (25.83) (4.01) (2.86) (1.75) SYMM2 NA 0.95 2.94 0.98 1.54 1.47 (NA) (0.18) (1.09) (0.38) (0.85) (0.66) (NA) (2.36) (6.8) (2.1) (2.56) (2.88) # 모의실험2 GLO distribution: quantile estimation with n=300 nboot=1000 n.sim=500 p=0.99 xi NCL Normal NBPct NBBCa SBPct PBOne PBTwo 0.4 0.9 ACL NA 0.782 0.784 0.864 0.904 0.828 LENGTH NA 131 136 123 108 80.2 (NA) (4.36) (4.71) (2.26) (1.26) (0.88) SYMM2 NA 0.77 0.85 0.9 0.7 0.67 (NA) (0.1) (0.1) (0.22) (0.24) (0.14) (NA) (2.33) (2.45) (1.78) (1.35) (1.68) 0.4 0.95 ACL NA 0.806 0.95 0.916 0.964 0.898 LENGTH NA 149 308 152 132 96.1 (NA) (5.11) (21.08) (2.92) (1.58) (1.06) SYMM2 NA 0.81 2.67 1.09 0.9 0.8 (NA) (0.16) (1.09) (0.4) (0.42) (0.29) (NA) (2.16) (6.02) (1.98) (1.55) (1.75) # 모의실험3 mixuni distribution: quantile estimation with n=300 nboot=1000 n.sim=500 p=0.99 xi NCL Normal NBPct NBBCa SBPct PBOne PBTwo 0.1 0.9 ACL NA 0.784 0.776 0.854 0.844 0.78 LENGTH NA 73.3 75.8 67.3 52 39.7 (NA) (2.54) (2.95) (1.26) (0.6) (0.43) SYMM2 NA 0.95 1.01 0.84 0.57 0.52 (NA) (0.06) (0.05) (0.25) (0.14) (0.04) (NA) (2.31) (2.79) (1.79) (1.26) (1.52) 0.1 0.95 ACL NA 0.806 0.932 0.91 0.91 0.862 LENGTH NA 83.5 155 83.3 63.3 47.5 (NA) (3.17) (6.98) (1.63) (0.74) (0.51) SYMM2 NA 0.98 2.52 1.05 0.74 0.71 (NA) (0.11) (0.98) (0.43) (0.3) (0.2) (NA) (2.28) (5.53) (2.1) (1.46) (1.65) # 모의실험4 mixbi distribution: quantile estimation with n=300 nboot=1000 n.sim=500 p=0.99 xi NCL Normal NBPct NBBCa SBPct PBOne PBTwo 0.1 0.9 ACL NA 0.784 0.78 0.852 0.604 0.126 LENGTH NA 30.7 31.5 30.5 60.1 44.1 (NA) (0.91) (0.97) (0.56) (0.65) (0.43) SYMM2 NA 0.73 0.8 0.85 4.68 -5.47 (NA) (0.12) (0.12) (0.3) (-13.63) (-8.56) (NA) (2.01) (2.4) (1.69) (14.3) (-4.01) 0.1 0.95 ACL NA 0.798 0.932 0.92 0.78 0.238 LENGTH NA 35.9 68.9 37.5 73.7 52.9 (NA) (1.77) (3.44) (0.71) (0.81) (0.53) SYMM2 NA 0.72 2.22 1.05 7.47 -7.11 (NA) (0.14) (0.95) (0.48) (2.61) (-12.11) (NA) (1.99) (4.99) (1.94) (16.38) (-4.2) ########### When n = 500 # 모의실험1 GEV distribution: quantile estimation with n=500 nboot=1000 n.sim=500 p=0.99 xi NCL Normal NBPct NBBCa SBPct PBOne PBTwo 0.1 0.9 ACL NA 0.872 0.862 0.916 0.938 0.888 LENGTH NA 23.7 22.8 22.6 22.1 16.6 (NA) (0.42) (0.42) (0.25) (0.16) (0.11) SYMM2 NA 1.05 1.09 0.94 1 1.09 (NA) (0.36) (0.36) (0.38) (0.43) (0.35) (NA) (2.05) (2.47) (1.88) (1.78) (2.65) 0.1 0.95 ACL NA 0.882 0.93 0.944 0.98 0.942 LENGTH NA 25.5 30.6 27.2 26.6 19.8 (NA) (0.43) (0.58) (0.3) (0.19) (0.14) SYMM2 NA 0.96 1.51 1.08 1.12 1.22 (NA) (0.34) (0.75) (0.5) (0.55) (0.48) (NA) (1.86) (2.76) (1.87) (1.83) (2.51) 0.2 0.9 ACL NA 0.836 0.828 0.89 0.938 0.854 LENGTH NA 35.6 34.4 34.5 34.8 25.4 (NA) (0.71) (0.71) (0.43) (0.29) (0.2) SYMM2 NA 0.92 0.96 0.82 0.92 0.84 (NA) (0.22) (0.21) (0.26) (0.4) (0.25) (NA) (2.03) (2.18) (1.79) (1.8) (2.34) 0.2 0.95 ACL NA 0.858 0.91 0.93 0.968 0.92 LENGTH NA 38.2 48.2 41.8 42.1 30.2 (NA) (0.74) (1.11) (0.54) (0.36) (0.24) SYMM2 NA 0.87 1.38 0.99 1.04 0.99 (NA) (0.28) (0.6) (0.4) (0.54) (0.4) (NA) (1.87) (2.88) (1.84) (1.92) (2.34) 0.3 0.9 ACL NA 0.87 0.862 0.908 0.978 0.916 LENGTH NA 58.1 57 54 56.1 39.5 (NA) (1.3) (1.33) (0.77) (0.46) (0.3) SYMM2 NA 1.01 1.06 0.88 1.11 1.16 (NA) (0.25) (0.26) (0.29) (0.57) (0.46) (NA) (2.19) (2.53) (1.78) (1.98) (2.74) 0.3 0.95 ACL NA 0.884 0.952 0.934 0.992 0.962 LENGTH NA 61.7 81.5 65.6 68.1 47.2 (NA) (1.33) (2.22) (0.95) (0.57) (0.36) SYMM2 NA 0.94 1.57 1.06 1.28 1.29 (NA) (0.29) (0.69) (0.43) (0.77) (0.61) (NA) (2.01) (3.25) (1.98) (2.04) (2.68) 0.4 0.9 ACL NA 0.858 0.85 0.886 0.976 0.884 LENGTH NA 95.4 92.5 82.4 88.1 59.9 (NA) (2.55) (2.52) (1.26) (0.83) (0.52) SYMM2 NA 0.89 0.95 0.76 1.14 1.1 (NA) (0.31) (0.3) (0.28) (0.58) (0.36) (NA) (2.37) (2.45) (1.54) (1.95) (2.43) 0.4 0.95 ACL NA 0.872 0.932 0.92 0.992 0.944 LENGTH NA 101 140 100 107 71.7 (NA) (2.58) (4.84) (1.58) (1.03) (0.64) SYMM2 NA 0.87 1.82 0.98 1.33 1.28 (NA) (0.32) (0.73) (0.45) (0.77) (0.55) (NA) (2.17) (3.48) (1.75) (2.15) (2.45) 0.5 0.95 ACL NA 0.88 0.938 0.93 0.996 0.946 LENGTH NA 169 236 157 174 111 (NA) (4.93) (8.4) (2.61) (1.79) (1.03) SYMM2 NA 1.11 2.01 1.07 1.49 1.35 (NA) (0.35) (0.8) (0.44) (0.9) (0.59) (NA) (2.54) (4.79) (2.03) (2.34) (2.71) # 모의실험2 GLO distribution: quantile estimation with n=500 nboot=1000 n.sim=500 p=0.99 xi NCL Normal NBPct NBBCa SBPct PBOne PBTwo 0.4 0.9 ACL NA 0.846 0.838 0.878 0.866 0.792 LENGTH NA 117 113 100 84.8 59.8 (NA) (2.95) (2.95) (1.49) (0.74) (0.49) SYMM2 NA 1 1.02 0.84 0.56 0.5 (NA) (0.29) (0.3) (0.27) (0.23) (0.07) (NA) (2.4) (2.63) (1.76) (1.1) (1.25) 0.4 0.95 ACL NA 0.856 0.934 0.922 0.93 0.838 LENGTH NA 124 170 122 103 71.5 (NA) (3.12) (4.95) (1.87) (0.92) (0.59) SYMM2 NA 0.96 1.82 1.02 0.74 0.62 (NA) (0.3) (0.74) (0.44) (0.38) (0.2) (NA) (2.17) (3.76) (1.97) (1.29) (1.28) # 모의실험3 mixuni distribution: quantile estimation with n=500 nboot=1000 n.sim=500 p=0.99 xi NCL Normal NBPct NBBCa SBPct PBOne PBTwo 0.1 0.9 ACL NA 0.846 0.834 0.878 0.816 0.726 LENGTH NA 64.3 63.2 54.9 41.3 30 (NA) (1.72) (1.79) (0.87) (0.37) (0.25) SYMM2 NA 1.09 1.16 0.88 0.47 0.4 (NA) (0.27) (0.24) (0.27) (0.1) (-0.04) (NA) (2.68) (2.98) (1.94) (1.08) (1.2) 0.1 0.95 ACL NA 0.852 0.938 0.942 0.894 0.792 LENGTH NA 68.3 93.3 67 49.8 35.8 (NA) (1.81) (3.16) (1.1) (0.45) (0.3) SYMM2 NA 0.95 1.82 1.08 0.62 0.52 (NA) (0.27) (0.66) (0.44) (0.24) (0.08) (NA) (2.44) (3.99) (2.15) (1.2) (1.25) # 모의실험4 mixbi distribution: quantile estimation with n=500 nboot=1000 n.sim=500 p=0.99 xi NCL Normal NBPct NBBCa SBPct PBOne PBTwo 0.1 0.9 ACL NA 0.864 0.854 0.89 0.174 0.018 LENGTH NA 28.2 27.2 24.7 48.4 33.9 (NA) (0.67) (0.66) (0.36) (0.38) (0.24) SYMM2 NA 1.15 1.23 0.99 -8.5 -3.69 (NA) (0.31) (0.32) (0.36) (-14.05) (-4.6) (NA) (2.5) (2.67) (1.96) (-5.94) (-3.18) 0.1 0.95 ACL NA 0.87 0.924 0.934 0.354 0.042 LENGTH NA 30 38.8 30.1 58.7 40.5 (NA) (0.69) (1.08) (0.45) (0.46) (0.3) SYMM2 NA 1.05 1.84 1.19 -11.1 -4.92 (NA) (0.31) (0.75) (0.51) (-20.8) (-6.56) (NA) (2.29) (3.61) (2.12) (12.03) (-4.04) ################# When n = 100 # 모의실험1 GEV distribution: quantile estimation with n=100 nboot=1000 n.sim=500 p=0.99 xi NCL NBPct NBBCa SBPct PBOne PBTwo 0.1 0.9 ACL 0.64 0.628 0.86 0.856 0.88 LENGTH 33.5 32.1 46.8 41.8 40.3 (0.97) (0.96) (0.92) (0.66) (0.63) SYMM2 0.38 0.34 0.85 0.67 1.08 (-0.19) (-0.21) (0.25) (0.21) (0.37) (1.28) (1.33) (1.8) (1.68) (2.93) 0.1 0.95 ACL 0.64 0.64 0.896 0.92 0.926 LENGTH 36.2 33.5 58.6 51.5 48.7 (0.98) (0.97) (1.22) (0.84) (0.76) SYMM2 0.32 0.36 1.12 0.91 1.25 (-0.17) (-0.19) (0.42) (0.37) (0.54) (1.07) (1.28) (2.14) (1.93) (2.96) 0.2 0.9 ACL 0.672 0.668 0.84 0.874 0.898 LENGTH 57.1 55.1 71.7 66.3 63.2 (2.28) (2.27) (1.54) (1.09) (1) SYMM2 0.48 0.49 0.88 0.89 1.38 (-0.18) (-0.19) (0.31) (0.32) (0.53) (1.39) (1.46) (1.81) (1.79) (3.05) 0.2 0.95 ACL 0.674 0.672 0.894 0.92 0.93 LENGTH 60.7 57 91.7 82.8 76.7 (2.29) (2.28) (2.16) (1.42) (1.23) SYMM2 0.42 0.48 1.21 1.17 1.58 (-0.16) (-0.18) (0.5) (0.51) (0.71) (1.17) (1.39) (2.26) (2.09) (3.14) 0.3 0.9 ACL 0.644 0.636 0.796 0.874 0.864 LENGTH 90.6 87.5 102 107 100 (4.35) (4.3) (2.54) (2.35) (2.14) SYMM2 0.29 0.3 0.74 0.89 1.23 (-0.24) (-0.26) (0.14) (0.31) (0.39) (1.48) (1.57) (1.68) (1.92) (3.09) 0.3 0.95 ACL 0.644 0.644 0.878 0.926 0.914 LENGTH 95 90.5 133 136 122 (4.36) (4.35) (3.53) (3.17) (2.64) SYMM2 0.26 0.29 1.08 1.23 1.53 (-0.22) (-0.24) (0.33) (0.54) (0.64) (1.32) (1.47) (2.13) (2.35) (3.29) 0.4 0.9 ACL 0.622 0.618 0.798 0.9 0.894 LENGTH 146 141 149 172 160 (7.91) (7.87) (3.76) (3.87) (3.4) SYMM2 0.34 0.35 0.68 1.21 1.66 (-0.26) (-0.29) (0.1) (0.42) (0.52) (1.6) (1.76) (1.68) (2.16) (3.53) 0.4 0.95 ACL 0.622 0.622 0.858 0.954 0.942 LENGTH 152 146 195 224 196 (7.95) (7.91) (5.26) (5.29) (4.26) SYMM2 0.31 0.34 1.08 1.61 1.99 (-0.26) (-0.26) (0.3) (0.71) (0.8) (1.44) (1.59) (2.25) (2.78) (3.83) 0.5 0.9 ACL 0.636 0.628 0.772 0.916 0.904 LENGTH 250 244 220 277 250 (17.17) (17.09) (6.16) (7.29) (6.07) SYMM2 0.35 0.34 0.61 1.2 1.63 (-0.26) (-0.3) (0.04) (0.43) (0.54) (1.87) (1.88) (1.57) (2.53) (4.11) 0.5 0.95 ACL 0.636 0.636 0.856 0.956 0.944 LENGTH 259 250 292 372 308 (17.18) (17.15) (8.75) (10.47) (7.58) SYMM2 0.32 0.35 0.99 1.69 1.97 (-0.25) (-0.26) (0.28) (0.78) (0.81) (1.67) (1.86) (2.21) (3.45) (4.5) # 모의실험2: xi here is the parameter of GLO GLO distribution: quantile estimation with n=100 nboot=1000 n.sim=500 p=0.99 xi NCL NBPct NBBCa SBPct PBOne PBTwo 0.4 0.9 ACL 0.654 0.648 0.796 0.816 0.838 LENGTH 177 172 184 165 155 (8.75) (8.69) (4.74) (3.65) (3.33) SYMM2 0.41 0.41 0.74 0.62 0.94 (-0.22) (-0.25) (0.14) (0.11) (0.2) (1.85) (2.01) (1.81) (1.57) (2.44) 0.4 0.95 ACL 0.66 0.654 0.846 0.884 0.884 LENGTH 186 177 241 210 189 (8.84) (8.75) (6.7) (4.9) (4.13) SYMM2 0.4 0.41 1.09 0.92 1.18 (-0.2) (-0.22) (0.37) (0.3) (0.38) (1.6) (1.85) (2.32) (2.01) (2.7) # 모의실험3 mixuni distribution: quantile estimation with n=100 nboot=1000 n.sim=500 p=0.99 xi NCL NBPct NBBCa SBPct PBOne PBTwo 0.1 0.9 ACL 0.694 0.684 0.822 0.8 0.842 LENGTH 100 97 103 81.1 77.1 (5.29) (5.26) (2.76) (1.62) (1.49) SYMM2 0.5 0.5 0.89 0.63 0.96 (-0.16) (-0.2) (0.19) (0.09) (0.19) (1.97) (2.06) (1.92) (1.45) (2.36) 0.1 0.95 ACL 0.694 0.692 0.87 0.876 0.89 LENGTH 105 100 135 102 93.8 (5.32) (5.28) (3.93) (2.12) (1.86) SYMM2 0.45 0.5 1.24 0.87 1.15 (-0.16) (-0.17) (0.4) (0.25) (0.36) (1.79) (1.98) (2.52) (1.75) (2.56) # 모의실험4 mixbi distribution: quantile estimation with n=100 nboot=1000 n.sim=500 p=0.99 xi NCL NBPct NBBCa SBPct PBOne PBTwo 0.1 0.9 ACL 0.622 0.622 0.778 0.972 0.652 LENGTH 43.6 42.4 44.7 91.8 86 (2.88) (2.86) (1.29) (1.73) (1.53) SYMM2 0.26 0.27 0.71 4.17 3.43 (-0.24) (-0.25) (0.06) (2.32) (-11.19) (1.49) (1.59) (1.83) (8.2) (11) 0.1 0.95 ACL 0.624 0.622 0.818 0.992 0.784 LENGTH 45.7 43.5 57.2 117 105 (2.88) (2.87) (1.79) (2.32) (1.91) SYMM2 0.23 0.26 1.01 4.61 5.47 (-0.22) (-0.24) (0.23) (2.84) (1.66) (1.34) (1.5) (2.21) (8.27) (13.12) ###### 추가 모의실험 pp=0.975 ###################################################################################### # 모의실험1; n=300 GEV distribution: quantile estimation with n=300 nboot=1000 n.sim=500 p=0.975 xi NCL NBPct NBBCa SBPct PBOne PBTwo 0.1 0.9 ACL 0.866 0.88 0.896 0.932 0.888 LENGTH 16.7 17.2 16.1 16.4 13.4 (0.27) (0.29) (0.15) (0.12) (0.1) SYMM2 0.83 0.97 0.74 0.93 0.97 (0.26) (0.34) (0.25) (0.38) (0.32) (1.84) (2.13) (1.5) (1.66) (2.04) 0.1 0.95 ACL 0.93 0.934 0.934 0.97 0.942 LENGTH 19.8 20.4 19.4 19.7 16.0 (0.3) (0.32) (0.18) (0.15) (0.12) SYMM2 0.92 1.11 0.85 1.02 1.06 (0.4) (0.5) (0.39) (0.5) (0.44) (1.98) (2.19) (1.56) (1.69) (1.93) 0.2 0.9 ACL 0.884 0.896 0.908 0.948 0.91 LENGTH 24.9 25.9 23.3 24.0 19.5 (0.47) (0.47) (0.25) (0.2) (0.16) SYMM2 0.94 1.04 0.76 0.98 1.03 (0.33) (0.42) (0.27) (0.42) (0.33) (1.88) (2.08) (1.55) (1.81) (2.19) 0.2 0.95 ACL 0.93 0.936 0.952 0.974 0.94 LENGTH 29.9 31.2 28 28.8 23.3 (0.55) (0.57) (0.31) (0.24) (0.19) SYMM2 1.04 1.25 0.91 1.12 1.11 (0.48) (0.61) (0.4) (0.55) (0.43) (1.96) (2.32) (1.62) (1.87) (2.11) 0.3 0.9 ACL 0.864 0.878 0.884 0.944 0.89 LENGTH 34.8 36.3 32.3 34.7 27.7 (0.65) (0.68) (0.36) (0.29) (0.23) SYMM2 0.89 1.08 0.7 1.03 1.02 (0.24) (0.36) (0.22) (0.5) (0.42) (2.1) (2.29) (1.59) (1.92) (2.35) 0.3 0.95 ACL 0.922 0.928 0.928 0.98 0.946 LENGTH 42 44.4 39 41.6 33.1 (0.75) (0.82) (0.45) (0.35) (0.27) SYMM2 1.04 1.28 0.86 1.12 1.17 (0.43) (0.57) (0.36) (0.67) (0.56) (2.13) (2.54) (1.66) (1.98) (2.35) 0.4 0.9 ACL 0.898 0.922 0.88 0.942 0.868 LENGTH 52.8 55.6 46.6 50.5 39.8 (1.04) (1.1) (0.58) (0.51) (0.39) SYMM2 1.14 1.35 0.81 1.1 1.1 (0.39) (0.48) (0.25) (0.49) (0.34) (2.37) (2.7) (1.77) (2.18) (2.59) 0.4 0.95 ACL 0.942 0.954 0.928 0.97 0.932 LENGTH 63.5 68 56.3 61 47.7 (1.26) (1.4) (0.72) (0.62) (0.46) SYMM2 1.31 1.55 0.96 1.27 1.25 (0.53) (0.67) (0.41) (0.64) (0.52) (2.5) (2.94) (1.91) (2.25) (2.6) 0.5 0.9 ACL 0.852 0.876 0.862 0.966 0.898 LENGTH 77.8 82.1 67.4 74.7 57.8 (1.7) (1.83) (0.94) (0.77) (0.57) SYMM2 1.29 1.49 0.94 1.29 1.26 (0.42) (0.52) (0.28) (0.62) (0.46) (2.85) (3.3) (1.95) (2.35) (2.78) 0.5 0.95 ACL 0.912 0.93 0.926 0.988 0.946 LENGTH 94.6 101 81.6 90.6 69.3 (2.07) (2.34) (1.16) (0.95) (0.69) SYMM2 1.46 1.77 1.1 1.47 1.44 (0.61) (0.72) (0.46) (0.81) (0.63) (2.92) (3.57) (2.11) (2.48) (2.75) # 모의실험2; n=300 GLO distribution: quantile estimation with n=300 nboot=1000 n.sim=500 p=0.975 xi NCL NBPct NBBCa SBPct PBOne PBTwo 0.4 0.9 ACL 0.886 0.9 0.894 0.928 0.876 LENGTH 64.3 68.5 57.4 54.6 43.7 (1.34) (1.45) (0.75) (0.5) (0.38) SYMM2 1.16 1.36 0.88 0.93 0.89 (0.41) (0.54) (0.31) (0.44) (0.37) (2.46) (3.03) (1.76) (1.9) (2.15) 0.4 0.95 ACL 0.934 0.94 0.936 0.974 0.928 LENGTH 78.5 84.4 69.3 65.8 52.2 (1.6) (1.82) (0.92) (0.6) (0.46) SYMM2 1.38 1.61 1.07 1.07 1.01 (0.63) (0.78) (0.47) (0.58) (0.52) (2.53) (3.07) (1.89) (1.97) (2.2) # 모의실험3; n=300 mixuni distribution: quantile estimation with n=300 nboot=1000 n.sim=500 p=0.975 xi NCL NBPct NBBCa SBPct PBOne PBTwo 0.1 0.9 ACL 0.876 0.884 0.872 0.916 0.854 LENGTH 33.9 35.9 31.6 28.5 23.1 (0.72) (0.81) (0.43) (0.25) (0.2) SYMM2 1.03 1.22 0.98 1.07 1.04 (0.32) (0.4) (0.31) (0.41) (0.26) (2.17) (2.56) (1.74) (1.94) (2.21) 0.1 0.95 ACL 0.934 0.95 0.916 0.968 0.894 LENGTH 41.3 44.3 38.3 34.3 27.6 (0.89) (1.04) (0.54) (0.31) (0.24) SYMM2 1.24 1.48 1.15 1.21 1.16 (0.54) (0.65) (0.46) (0.54) (0.4) (2.4) (2.9) (1.92) (2) (2.24) # 모의실험4; n=300 mixbi distribution: quantile estimation with n=300 nboot=1000 n.sim=500 p=0.975 xi NCL NBPct NBBCa SBPct PBOne PBTwo 0.1 0.9 ACL 0.862 0.878 0.876 0.538 0.228 LENGTH 15.2 16.1 14.8 29.5 23.5 (0.31) (0.32) (0.19) (0.26) (0.19) SYMM2 0.89 1.19 0.84 2.46 -5.06 (0.26) (0.34) (0.31) (-11.56) (-8.59) (2.39) (2.75) (1.96) (9.42) (-3.37) 0.1 0.95 ACL 0.92 0.94 0.924 0.704 0.368 LENGTH 18.5 19.6 17.9 35.6 28.1 (0.34) (0.38) (0.23) (0.31) (0.23) SYMM2 1.16 1.41 1 4.96 -6.1 (0.38) (0.54) (0.45) (-11.96) (-11.36) (2.55) (3.1) (1.99) (12.76) (5.74) # 모의실험1; n=100 GEV distribution: quantile estimation with n=100 nboot=1000 n.sim=500 p=0.975 xi NCL NBPct NBBCa SBPct PBOne PBTwo 0.1 0.9 ACL 0.882 0.884 0.88 0.876 0.878 LENGTH 32 31.7 28.4 27.3 24.8 (0.75) (0.76) (0.43) (0.37) (0.33) SYMM2 1.01 1.12 0.81 0.86 1.05 (0.34) (0.33) (0.28) (0.28) (0.32) (2.24) (2.45) (1.66) (1.81) (2.6) 0.1 0.95 ACL 0.902 0.936 0.944 0.93 0.922 LENGTH 34.6 40.8 34.6 32.9 29.8 (0.79) (1.1) (0.54) (0.45) (0.4) SYMM2 1.01 1.46 0.98 1.01 1.15 (0.33) (0.56) (0.45) (0.43) (0.47) (2.07) (2.97) (1.81) (1.95) (2.51) 0.2 0.9 ACL 0.864 0.862 0.852 0.886 0.854 LENGTH 45.3 45.2 38.3 39.2 35.6 (1.23) (1.34) (0.65) (0.63) (0.56) SYMM2 1.03 1.11 0.72 0.94 1.09 (0.28) (0.29) (0.21) (0.29) (0.25) (2.6) (2.86) (1.67) (1.94) (2.5) 0.2 0.95 ACL 0.874 0.91 0.908 0.934 0.924 LENGTH 48.8 57.7 46.9 47.8 42.9 (1.29) (1.85) (0.81) (0.79) (0.69) SYMM2 1.01 1.44 0.93 1.12 1.26 (0.28) (0.53) (0.36) (0.44) (0.47) (2.27) (3.14) (1.85) (2.09) (2.7) 0.3 0.9 ACL 0.848 0.854 0.856 0.898 0.876 LENGTH 70.4 70.9 52.3 56.9 51.1 (4.37) (4.44) (0.94) (0.91) (0.79) SYMM2 1.08 1.2 0.69 0.99 1.16 (0.31) (0.35) (0.18) (0.43) (0.44) (2.55) (2.87) (1.61) (2.08) (2.68) 0.3 0.95 ACL 0.87 0.912 0.918 0.952 0.938 LENGTH 75.4 94.3 64.6 69.9 61.8 (4.41) (8.04) (1.21) (1.16) (0.97) SYMM2 1.09 1.54 0.92 1.2 1.38 (0.33) (0.59) (0.37) (0.61) (0.64) (2.44) (3.54) (1.81) (2.31) (2.81) 0.4 0.9 ACL 0.84 0.842 0.806 0.91 0.888 LENGTH 108 108 71.5 82.3 72.9 (5.55) (5.57) (1.42) (1.47) (1.24) SYMM2 1.24 1.35 0.72 1.04 1.18 (0.3) (0.33) (0.11) (0.44) (0.39) (2.94) (3.23) (1.63) (2.24) (2.91) 0.4 0.95 ACL 0.852 0.9 0.878 0.948 0.932 LENGTH 117 149 88.5 102 88.7 (6.93) (9.71) (1.8) (1.88) (1.54) SYMM2 1.22 1.69 0.98 1.32 1.39 (0.35) (0.55) (0.3) (0.64) (0.58) (2.76) (3.96) (1.94) (2.47) (3.01) 0.5 0.9 ACL 0.894 0.9 0.846 0.946 0.908 LENGTH 188 188 105 134 116 (9.01) (9.07) (2.08) (2.67) (2.15) SYMM2 1.95 2.09 0.9 1.52 1.69 (0.51) (0.53) (0.23) (0.69) (0.65) (4.25) (4.82) (1.8) (3.03) (3.75) 0.5 0.95 ACL 0.906 0.932 0.912 0.972 0.958 LENGTH 199 257 133 169 142 (9.26) (15.71) (2.73) (3.52) (2.67) SYMM2 1.86 2.61 1.21 1.86 2.02 (0.53) (0.84) (0.42) (0.97) (0.93) (3.82) (5.7) (2.21) (3.36) (3.95) # 모의실험2; n=100, pp=0.975 GLO distribution: quantile estimation with n=100 nboot=1000 n.sim=500 p=0.975 xi NCL NBPct NBBCa SBPct PBOne PBTwo 0.4 0.9 ACL 0.88 0.876 0.85 0.884 0.884 LENGTH 133 134 91 88.8 79.7 (5.37) (5.41) (1.81) (1.45) (1.28) SYMM2 1.42 1.54 0.82 0.92 1.09 (0.36) (0.41) (0.25) (0.35) (0.39) (3.28) (3.53) (1.67) (1.95) (2.6) 0.4 0.95 ACL 0.886 0.92 0.908 0.934 0.928 LENGTH 142 179 113 109 96.4 (5.49) (8.55) (2.38) (1.83) (1.56) SYMM2 1.36 1.9 1.1 1.14 1.24 (0.38) (0.68) (0.43) (0.53) (0.54) (2.97) (4.48) (2.01) (2.15) (2.63) # 모의실험3; n=100, pp=0.975 mixuni distribution: quantile estimation with n=100 nboot=1000 n.sim=500 p=0.975 xi NCL NBPct NBBCa SBPct PBOne PBTwo 0.1 0.9 ACL 0.862 0.858 0.848 0.87 0.852 LENGTH 77 77 52.4 47.5 43 (3.45) (3.5) (1.12) (0.82) (0.72) SYMM2 1.34 1.46 0.84 0.95 1.1 (0.32) (0.36) (0.25) (0.3) (0.33) (3.44) (3.72) (1.92) (2.07) (2.7) 0.1 0.95 ACL 0.88 0.918 0.91 0.926 0.91 LENGTH 84 106 65 58 51.8 (4.55) (5.87) (1.42) (1.04) (0.87) SYMM2 1.39 1.94 1.07 1.13 1.27 (0.37) (0.64) (0.41) (0.49) (0.49) (3.21) (4.54) (2.22) (2.34) (2.76) # 모의실험4; n=100, pp=0.975 mixbi distribution: quantile estimation with n=100 nboot=1000 n.sim=500 p=0.975 xi NCL NBPct NBBCa SBPct PBOne PBTwo 0.1 0.9 ACL 0.846 0.842 0.852 0.924 0.74 LENGTH 33.1 33.2 24.8 49 44.0 (1.27) (1.3) (0.51) (0.77) (0.67) SYMM2 1.22 1.3 0.93 3.7 3.53 (0.28) (0.32) (0.28) (1.82) (-6) (3.23) (3.4) (2.12) (7.33) (8.98) 0.1 0.95 ACL 0.86 0.902 0.896 0.976 0.856 LENGTH 35.3 44.2 30.4 60.7 53.4 (1.29) (1.8) (0.65) (1) (0.82) SYMM2 1.24 1.77 1.11 4.03 4.62 (0.35) (0.58) (0.43) (2.43) (1.85) (2.94) (4.06) (2.31) (7.11) (9.46) # 모의실험1; n=500, pp=0.975 GEV distribution: quantile estimation with n=500 nboot=1000 n.sim=500 p=0.975 xi NCL NBPct NBBCa SBPct PBOne PBTwo 0.1 0.9 ACL 0.902 0.902 0.916 0.948 0.912 LENGTH 12.8 12.9 12.7 13 10.4 (0.18) (0.18) (0.09) (0.07) (0.06) SYMM2 0.84 0.88 0.79 0.92 0.88 (0.33) (0.34) (0.33) (0.46) (0.37) (1.69) (1.8) (1.45) (1.65) (1.94) 0.1 0.95 ACL 0.93 0.936 0.966 0.984 0.956 LENGTH 15.3 15.6 15.2 15.5 12.3 (0.2) (0.21) (0.11) (0.09) (0.07) SYMM2 0.91 0.99 0.88 1 1.02 (0.43) (0.5) (0.46) (0.56) (0.5) (1.69) (1.87) (1.48) (1.64) (1.93) 0.2 0.9 ACL 0.888 0.88 0.908 0.952 0.908 LENGTH 19.3 19.4 18.4 18.8 14.9 (0.29) (0.29) (0.15) (0.11) (0.09) SYMM2 0.92 0.96 0.78 0.93 0.94 (0.32) (0.36) (0.29) (0.47) (0.36) (1.92) (2.07) (1.52) (1.71) (2.02) 0.2 0.95 ACL 0.922 0.928 0.96 0.986 0.952 LENGTH 22.8 23.4 22.1 22.5 17.7 (0.32) (0.34) (0.19) (0.13) (0.1) SYMM2 1 1.12 0.92 1.03 1.02 (0.42) (0.52) (0.43) (0.59) (0.51) (1.92) (2.19) (1.58) (1.74) (2.01) 0.3 0.9 ACL 0.888 0.888 0.91 0.956 0.898 LENGTH 27.2 27.6 26.5 27.5 21.4 (0.42) (0.43) (0.26) (0.19) (0.14) SYMM2 0.87 0.94 0.75 1.01 1.01 (0.27) (0.3) (0.32) (0.52) (0.41) (2.14) (2.3) (1.68) (1.98) (2.27) 0.3 0.95 ACL 0.932 0.95 0.952 0.986 0.942 LENGTH 32.7 33.8 31.8 32.9 25.6 (0.48) (0.49) (0.31) (0.23) (0.17) SYMM2 1.01 1.15 0.89 1.15 1.12 (0.47) (0.54) (0.43) (0.68) (0.54) (2.12) (2.4) (1.72) (2.02) (2.33) 0.4 0.9 ACL 0.882 0.888 0.884 0.966 0.894 LENGTH 40.0 40.8 37.4 39.5 30.3 (0.65) (0.66) (0.38) (0.29) (0.21) SYMM2 1 1.13 0.84 1.08 1.04 (0.35) (0.39) (0.29) (0.55) (0.41) (2.19) (2.31) (1.74) (1.97) (2.31) 0.4 0.95 ACL 0.94 0.948 0.958 0.986 0.958 LENGTH 47.8 49.6 45 47.5 36.1 (0.73) (0.79) (0.46) (0.35) (0.25) SYMM2 1.18 1.33 0.99 1.19 1.19 (0.53) (0.59) (0.43) (0.68) (0.58) (2.18) (2.44) (1.81) (1.97) (2.27) 0.5 0.9 ACL 0.88 0.88 0.886 0.964 0.884 LENGTH 59 59.7 53.3 57.9 43.5 (0.97) (1) (0.61) (0.48) (0.35) SYMM2 1.09 1.15 0.85 1.16 1.05 (0.37) (0.4) (0.3) (0.57) (0.38) (2.49) (2.69) (1.86) (2.39) (2.67) 0.5 0.95 ACL 0.924 0.924 0.922 0.988 0.946 LENGTH 70.3 72.8 64.1 69.9 52 (1.13) (1.19) (0.75) (0.59) (0.42) SYMM2 1.26 1.36 1 1.28 1.23 (0.54) (0.65) (0.46) (0.72) (0.56) (2.49) (2.77) (1.96) (2.44) (2.72) # 모의실험2; n=500, pp=0.975 GLO distribution: quantile estimation with n=500 nboot=1000 n.sim=500 p=0.975 xi NCL NBPct NBBCa SBPct PBOne PBTwo 0.4 0.9 ACL 0.866 0.872 0.9 0.92 0.858 LENGTH 48.8 49.5 45.8 42 32.8 (0.85) (0.87) (0.5) (0.3) (0.23) SYMM2 0.95 1.07 0.83 0.86 0.85 (0.32) (0.36) (0.27) (0.31) (0.21) (2.22) (2.32) (1.8) (1.68) (1.97) 0.4 0.95 ACL 0.912 0.918 0.938 0.958 0.922 LENGTH 58.1 60.4 55.1 50.4 39.2 (0.97) (1.02) (0.6) (0.37) (0.27) SYMM2 1.1 1.26 1.01 0.99 0.95 (0.49) (0.6) (0.42) (0.44) (0.33) (2.28) (2.58) (1.89) (1.74) (1.93) # 모의실험3; n=500, pp=0.975 mixuni distribution: quantile estimation with n=500 nboot=1000 n.sim=500 p=0.975 xi NCL NBPct NBBCa SBPct PBOne PBTwo 0.1 0.9 ACL 0.87 0.874 0.926 0.922 0.85 LENGTH 25.9 26.4 25.3 22.2 17.6 (0.45) (0.46) (0.26) (0.16) (0.12) SYMM2 0.95 1.01 0.92 0.92 0.84 (0.35) (0.4) (0.35) (0.36) (0.23) (2.07) (2.38) (1.86) (1.89) (2.26) 0.1 0.95 ACL 0.912 0.926 0.964 0.972 0.908 LENGTH 31.3 32.4 30.4 26.6 21 (0.51) (0.53) (0.32) (0.19) (0.14) SYMM2 1.16 1.28 1.04 1.03 0.99 (0.55) (0.61) (0.49) (0.52) (0.37) (2.22) (2.55) (1.9) (1.92) (2.19) # 모의실험4; n=500, pp=0.975 mixbi distribution: quantile estimation with n=500 nboot=1000 n.sim=500 p=0.975 xi NCL NBPct NBBCa SBPct PBOne PBTwo 0.1 0.9 ACL 0.866 0.882 0.912 0.178 0.048 LENGTH 12.4 12.6 12.2 23.2 18.1 (0.21) (0.22) (0.12) (0.15) (0.11) SYMM2 1.01 1.13 0.98 -6.54 -4.02 (0.34) (0.42) (0.36) (-11.26) (-5.49) (2.11) (2.26) (1.95) (-4.59) (-3.27) 0.1 0.95 ACL 0.92 0.922 0.964 0.334 0.102 LENGTH 14.8 15.4 14.6 27.8 21.5 (0.24) (0.25) (0.15) (0.18) (0.13) SYMM2 1.22 1.35 1.13 -8.38 -5.23 (0.52) (0.62) (0.52) (-16.01) (-7.91) (2.23) (2.43) (2.09) (7.4) (-3.97) ###### 추가 모의실험 pp=0.995 ###################################################################################### # 모의실험1; n=300 GEV distribution: quantile estimation with n=300 nboot=1000 n.sim=500 p=0.995 xi NCL NBPct NBBCa SBPct PBOne PBTwo 0.1 0.9 ACL 0.782 0.778 0.874 0.904 0.872 LENGTH 40.7 39.6 43 37.9 29.9 (1.13) (1.13) (0.81) (0.41) (0.29) SYMM2 0.76 0.78 0.89 0.83 1.06 (0.1) (0.08) (0.27) (0.37) (0.37) (2.01) (2.16) (1.88) (1.62) (2.7) 0.1 0.95 ACL 0.786 0.782 0.916 0.942 0.914 LENGTH 43 41.1 52.9 46.1 35.9 (1.14) (1.13) (1.04) (0.51) (0.36) SYMM2 0.7 0.74 1.12 0.97 1.2 (0.1) (0.1) (0.42) (0.53) (0.53) (1.75) (1.96) (2.17) (1.82) (2.61) 0.2 0.9 ACL 0.754 0.752 0.834 0.92 0.88 LENGTH 64.2 62.5 65.6 64.4 48.3 (2.49) (2.49) (1.36) (0.78) (0.53) SYMM2 0.65 0.69 0.85 0.91 1.1 (0.02) (0) (0.2) (0.41) (0.37) (1.75) (1.97) (1.76) (1.89) (2.94) 0.2 0.95 ACL 0.758 0.758 0.892 0.968 0.92 LENGTH 67.6 64.8 81.5 79.1 58 (2.51) (2.49) (1.8) (0.98) (0.64) SYMM2 0.58 0.65 1.08 1.14 1.22 (0.04) (0.04) (0.35) (0.58) (0.5) (1.52) (1.76) (2.01) (2.09) (2.75) 0.3 0.9 ACL 0.74 0.734 0.828 0.95 0.902 LENGTH 134 132 114 112 79.7 (6.8) (6.81) (2.71) (1.51) (0.96) SYMM2 0.93 0.95 0.94 1.16 1.27 (-0.02) (-0.03) (0.19) (0.51) (0.45) (2.5) (2.67) (1.94) (2.05) (3.09) 0.3 0.95 ACL 0.75 0.74 0.884 0.972 0.938 LENGTH 139 135 143 140 95.8 (6.82) (6.83) (3.61) (1.94) (1.16) SYMM2 0.87 0.9 1.18 1.41 1.49 (0) (-0.02) (0.4) (0.76) (0.62) (2.31) (2.49) (2.38) (2.35) (3.01) 0.4 0.9 ACL 0.778 0.776 0.814 0.962 0.898 LENGTH 206 202 173 191 128 (8.5) (8.5) (3.97) (2.74) (1.66) SYMM2 0.88 0.88 0.77 1.11 1.16 (0.09) (0.09) (0.21) (0.6) (0.46) (2.37) (2.54) (1.71) (2.08) (2.75) 0.4 0.95 ACL 0.78 0.778 0.878 0.988 0.944 LENGTH 213 207 220 242 155 (8.55) (8.52) (5.29) (3.62) (2.01) SYMM2 0.79 0.85 1.06 1.48 1.35 (0.08) (0.09) (0.43) (0.91) (0.67) (2.2) (2.3) (2.14) (2.48) (2.91) 0.5 0.9 ACL 0.714 0.704 0.77 0.978 0.898 LENGTH 443 437 286 338 214 (28.51) (28.46) (8.19) (5.3) (2.94) SYMM2 0.81 0.8 0.7 1.51 1.45 (-0.1) (-0.12) (0.04) (0.79) (0.53) (3.16) (3.09) (1.86) (2.43) (3.16) 0.5 0.95 ACL 0.718 0.714 0.84 0.994 0.942 LENGTH 455 446 371 436 259 (28.61) (28.52) (11.28) (7.18) (3.57) SYMM2 0.8 0.83 1.06 1.97 1.65 (-0.08) (-0.1) (0.26) (1.12) (0.74) (2.72) (2.92) (2.31) (2.99) (3.2) # 모의실험2; n=300 GLO distribution: quantile estimation with n=300 nboot=1000 n.sim=500 p=0.995 xi NCL NBPct NBBCa SBPct PBOne PBTwo 0.4 0.9 ACL 0.776 0.774 0.834 0.836 0.772 LENGTH 305 300 221 174 124 (17.77) (17.77) (5.7) (2.48) (1.57) SYMM2 0.94 0.96 0.82 0.6 0.52 (0.08) (0.07) (0.22) (0.17) (0.06) (2.77) (3.02) (1.9) (1.16) (1.4) 0.4 0.95 ACL 0.778 0.778 0.902 0.948 0.848 LENGTH 314 306 284 217 149 (17.81) (17.8) (7.82) (3.21) (1.92) SYMM2 0.84 0.92 1.11 0.84 0.68 (0.09) (0.09) (0.38) (0.38) (0.2) (2.5) (2.69) (2.34) (1.46) (1.48) # 모의실험3; n=300 mixuni distribution: quantile estimation with n=300 nboot=1000 n.sim=500 p=0.995 xi NCL NBPct NBBCa SBPct PBOne PBTwo 0.1 0.9 ACL 0.758 0.754 0.822 0.746 0.708 LENGTH 158 156 120 77.7 58.1 (7.36) (7.37) (2.91) (1.02) (0.7) SYMM2 1.05 1.06 0.84 0.33 0.31 (0.05) (0.03) (0.22) (-0.01) (-0.09) (3.21) (3.35) (2.15) (0.88) (1.03) 0.1 0.95 ACL 0.762 0.76 0.87 0.838 0.768 LENGTH 163 159 154 95.6 69.7 (7.37) (7.38) (3.96) (1.3) (0.85) SYMM2 0.99 1.06 1.2 0.54 0.46 (0.05) (0.06) (0.45) (0.15) (0.03) (2.77) (3.1) (2.61) (1.1) (1.17) # 모의실험4; n=300 mixbi distribution: quantile estimation with n=300 nboot=1000 n.sim=500 p=0.995 xi NCL NBPct NBBCa SBPct PBOne PBTwo 0.1 0.9 ACL 0.758 0.756 0.776 0.734 0.186 LENGTH 64.7 63.8 49.5 97.9 68.7 (5.03) (5.02) (1.34) (1.27) (0.79) SYMM2 0.84 0.88 0.7 5.6 -5.38 (0.02) (0.01) (0.07) (-11.93) (-8.74) (2.37) (2.5) (1.88) (15.34) (-3.96) 0.1 0.95 ACL 0.76 0.758 0.856 0.868 0.288 LENGTH 67 65.3 62.1 123 82.6 (5.04) (5.03) (1.77) (1.65) (0.96) SYMM2 0.75 0.82 0.94 7.71 -6.96 (0.02) (0.02) (0.21) (3.77) (-11.52) (2.09) (2.31) (2.28) (16.44) (3.91) # 모의실험1; n=100 GEV distribution: quantile estimation with n=100 nboot=1000 n.sim=500 p=0.995 xi NCL NBPct NBBCa SBPct PBOne PBTwo 0.1 0.9 ACL 0.378 0.378 0.782 0.82 0.868 LENGTH 28.8 26.2 66.4 53.9 55.2 (1) (0.98) (1.94) (1.01) (0.94) SYMM2 -0.24 -0.25 0.93 0.67 1.2 (-0.51) (-0.55) (0.07) (0.14) (0.42) (0.29) (0.33) (1.91) (1.36) (2.55) 0.1 0.95 ACL 0.378 0.378 0.822 0.87 0.91 LENGTH 31.2 27.6 86.3 66.7 67.1 (1) (0.98) (2.82) (1.31) (1.16) SYMM2 -0.21 -0.24 1.23 0.88 1.4 (-0.48) (-0.52) (0.21) (0.31) (0.59) (0.26) (0.33) (2.37) (1.65) (2.71) 0.2 0.9 ACL 0.396 0.388 0.78 0.858 0.88 LENGTH 48.1 44.3 110 96.2 93.9 (2.22) (2.18) (3.83) (2.19) (1.9) SYMM2 -0.22 -0.26 0.83 0.85 1.39 (-0.56) (-0.61) (0.03) (0.23) (0.48) (0.42) (0.46) (2.17) (1.79) (3.03) 0.2 0.95 ACL 0.396 0.396 0.822 0.9 0.92 LENGTH 51.5 46.4 149 124 115 (2.25) (2.2) (6.02) (3.06) (2.36) SYMM2 -0.21 -0.24 1.18 1.16 1.64 (-0.53) (-0.58) (0.23) (0.43) (0.7) (0.35) (0.44) (2.84) (2.2) (3.26) 0.3 0.9 ACL 0.37 0.368 0.766 0.892 0.892 LENGTH 76.8 72.2 174 174 158 (3.46) (3.42) (6.12) (4.45) (3.49) SYMM2 -0.26 -0.28 0.79 1 1.4 (-0.59) (-0.62) (0.05) (0.35) (0.5) (0.34) (0.35) (1.97) (2.2) (3.42) 0.3 0.95 ACL 0.37 0.37 0.828 0.934 0.94 LENGTH 81.7 74.8 242 232 194 (3.49) (3.43) (9.88) (6.43) (4.33) SYMM2 -0.23 -0.26 1.24 1.49 1.81 (-0.56) (-0.6) (0.24) (0.65) (0.8) (0.3) (0.34) (2.85) (3.01) (3.71) 0.4 0.9 ACL 0.398 0.394 0.754 0.9 0.882 LENGTH 133 126 298 316 265 (7.02) (6.97) (11.54) (9.67) (6.79) SYMM2 -0.21 -0.23 1 1.25 1.48 (-0.6) (-0.64) (0.01) (0.46) (0.54) (0.46) (0.51) (2.43) (2.72) (3.75) 0.4 0.95 ACL 0.398 0.398 0.818 0.946 0.936 LENGTH 140 130 437 443 329 (7.12) (6.99) (19.37) (14.96) (8.57) SYMM2 -0.2 -0.21 1.55 1.88 1.92 (-0.57) (-0.61) (0.21) (0.84) (0.83) (0.45) (0.5) (3.52) (3.82) (4.33) 0.5 0.9 ACL 0.364 0.362 0.778 0.948 0.926 LENGTH 221 210 448 575 446 (19.36) (19.29) (17.6) (18.77) (12.13) SYMM2 -0.28 -0.32 0.9 1.57 1.78 (-0.62) (-0.65) (0.09) (0.68) (0.72) (0.34) (0.35) (2.14) (3.37) (4.32) 0.5 0.95 ACL 0.366 0.362 0.828 0.978 0.964 LENGTH 231 216 684 859 560 (19.41) (19.31) (33.31) (34.14) (15.52) SYMM2 -0.26 -0.3 1.45 2.42 2.18 (-0.59) (-0.63) (0.37) (1.22) (0.99) (0.31) (0.33) (3.59) (5.1) (4.66) # 모의실험2; n=100 GLO distribution: quantile estimation with n=100 nboot=1000 n.sim=500 p=0.995 xi NCL NBPct NBBCa SBPct PBOne PBTwo 0.4 0.9 ACL 0.396 0.394 0.766 0.798 0.842 LENGTH 160 150 344 265 242 (12.39) (12.32) (12.69) (6.39) (5.16) SYMM2 -0.25 -0.28 0.93 0.69 1 (-0.61) (-0.63) (0.04) (0.11) (0.27) (0.57) (0.6) (2.36) (1.61) (2.42) 0.4 0.95 ACL 0.396 0.396 0.828 0.872 0.904 LENGTH 168 155 499 354 298 (12.46) (12.36) (21.9) (9.36) (6.5) SYMM2 -0.24 -0.25 1.49 1.1 1.28 (-0.57) (-0.62) (0.28) (0.36) (0.47) (0.51) (0.57) (3.38) (2.33) (2.77) # 모의실험3; n=100 mixuni distribution: quantile estimation with n=100 nboot=1000 n.sim=500 p=0.995 xi NCL NBPct NBBCa SBPct PBOne PBTwo 0.1 0.9 ACL 0.39 0.388 0.742 0.67 0.758 LENGTH 87.9 83.1 188 114 111 (4.97) (4.9) (7.67) (2.85) (2.52) SYMM2 -0.26 -0.27 0.77 0.32 0.6 (-0.61) (-0.64) (-0.02) (-0.13) (0.02) (0.46) (0.5) (2.41) (1.19) (1.83) 0.1 0.95 ACL 0.392 0.39 0.8 0.77 0.814 LENGTH 92.6 85.6 268 147 136 (5.01) (4.92) (12.51) (3.98) (3.12) SYMM2 -0.24 -0.26 1.21 0.6 0.82 (-0.58) (-0.62) (0.19) (0.04) (0.18) (0.42) (0.48) (3.36) (1.56) (2) # 모의실험4; n=100 mixbi distribution: quantile estimation with n=100 nboot=1000 n.sim=500 p=0.995 xi NCL NBPct NBBCa SBPct PBOne PBTwo 0.1 0.9 ACL 0.43 0.424 0.694 0.986 0.616 LENGTH 40.8 38.4 79.1 157 139 (1.94) (1.91) (3.2) (3.85) (2.94) SYMM2 -0.14 -0.17 0.69 4.51 2.49 (-0.56) (-0.59) (-0.12) (2.2) (-13.13) (0.7) (0.76) (2.4) (10.72) (8.45) 0.1 0.95 ACL 0.434 0.428 0.748 0.998 0.758 LENGTH 43.2 39.7 110 213 172 (1.96) (1.91) (5) (5.75) (3.72) SYMM2 -0.12 -0.15 1.02 5.51 4.66 (-0.54) (-0.57) (0) (2.84) (0.63) (0.64) (0.74) (3.33) (11.49) (12.56) # 모의실험1; n=500 GEV distribution: quantile estimation with n=500 nboot=1000 n.sim=500 p=0.995 xi NCL NBPct NBBCa SBPct PBOne PBTwo 0.1 0.9 ACL 0.858 0.85 0.892 0.958 0.878 LENGTH 34.5 34.1 32.6 30.8 22.6 (0.8) (0.82) (0.51) (0.26) (0.17) SYMM2 0.93 0.99 0.93 0.79 0.87 (0.28) (0.29) (0.3) (0.43) (0.32) (2.08) (2.26) (1.7) (1.59) (2.15) 0.1 0.95 ACL 0.87 0.91 0.932 0.978 0.938 LENGTH 38 44.8 39.5 37.2 27 (0.94) (1.29) (0.63) (0.31) (0.2) SYMM2 0.93 1.32 1.06 0.93 0.99 (0.3) (0.58) (0.43) (0.57) (0.49) (1.83) (2.8) (1.86) (1.68) (2.21) 0.2 0.9 ACL 0.864 0.87 0.892 0.952 0.888 LENGTH 60.6 60 53.7 53.5 37.2 (1.51) (1.6) (0.87) (0.49) (0.3) SYMM2 1.05 1.15 1 1.05 1.19 (0.33) (0.37) (0.32) (0.52) (0.4) (2.31) (2.48) (1.81) (1.85) (2.65) 0.2 0.95 ACL 0.882 0.92 0.924 0.978 0.938 LENGTH 65.9 79.5 65.3 65 44.5 (1.65) (2.49) (1.08) (0.6) (0.36) SYMM2 1 1.53 1.18 1.22 1.33 (0.36) (0.59) (0.48) (0.69) (0.59) (2.11) (3.04) (1.99) (1.98) (2.62) 0.3 0.9 ACL 0.862 0.862 0.862 0.976 0.892 LENGTH 115 115 90 90.7 59.9 (4.65) (4.76) (1.73) (0.91) (0.54) SYMM2 1.23 1.29 0.88 1.1 1.13 (0.33) (0.36) (0.26) (0.54) (0.36) (2.82) (3.02) (1.8) (1.86) (2.67) 0.3 0.95 ACL 0.88 0.93 0.902 0.996 0.942 LENGTH 123 157 111 111 71.6 (4.74) (8.14) (2.24) (1.13) (0.65) SYMM2 1.18 1.75 1.07 1.32 1.28 (0.37) (0.68) (0.44) (0.76) (0.52) (2.59) (3.81) (2.08) (2.08) (2.53) 0.4 0.9 ACL 0.846 0.85 0.854 0.986 0.892 LENGTH 213 215 145 154 96.5 (14.14) (14.53) (2.98) (1.66) (0.94) SYMM2 1.29 1.39 0.84 1.09 1 (0.4) (0.43) (0.28) (0.6) (0.4) (3.26) (3.7) (1.72) (1.97) (2.54) 0.4 0.95 ACL 0.856 0.898 0.892 0.996 0.95 LENGTH 228 303 180 191 116 (14.21) (26.05) (3.91) (2.1) (1.13) SYMM2 1.29 1.93 1.12 1.36 1.2 (0.41) (0.69) (0.46) (0.85) (0.58) (2.94) (4.33) (2.03) (2.25) (2.74) 0.5 0.9 ACL 0.866 0.878 0.858 0.988 0.896 LENGTH 396 399 240 269 161 (19.89) (20.01) (4.76) (3.06) (1.68) SYMM2 1.58 1.76 0.85 1.34 1.23 (0.43) (0.48) (0.25) (0.79) (0.44) (3.92) (4.28) (1.89) (2.32) (3.1) 0.5 0.95 ACL 0.884 0.91 0.912 0.998 0.946 LENGTH 418 568 300 337 192 (20.29) (36.76) (6.21) (3.98) (2.01) SYMM2 1.55 2.31 1.14 1.68 1.36 (0.41) (0.75) (0.44) (1.04) (0.63) (3.63) (5.22) (2.28) (2.67) (2.93) # 모의실험2; n=500 GLO distribution: quantile estimation with n=500 nboot=1000 n.sim=500 p=0.995 xi NCL NBPct NBBCa SBPct PBOne PBTwo 0.4 0.9 ACL 0.846 0.834 0.844 0.85 0.76 LENGTH 244 247 175 138 91.2 (10.13) (10.43) (3.72) (1.33) (0.8) SYMM2 1.27 1.34 0.83 0.51 0.4 (0.26) (0.26) (0.17) (0.18) (0.01) (3.14) (3.29) (1.76) (0.95) (0.97) 0.4 0.95 ACL 0.864 0.902 0.898 0.924 0.818 LENGTH 264 342 217 169 109 (10.85) (17.32) (4.75) (1.66) (0.97) SYMM2 1.22 1.85 1.08 0.72 0.5 (0.28) (0.57) (0.35) (0.35) (0.13) (2.95) (4.26) (2.11) (1.18) (1.08) # 모의실험3; n=500 mixuni distribution: quantile estimation with n=500 nboot=1000 n.sim=500 p=0.995 xi NCL NBPct NBBCa SBPct PBOne PBTwo 0.1 0.9 ACL 0.878 0.886 0.878 0.756 0.62 LENGTH 142 142 96.6 63.7 44.1 (5.8) (5.89) (1.97) (0.66) (0.41) SYMM2 1.33 1.44 0.84 0.25 0.13 (0.39) (0.45) (0.27) (0.01) (-0.14) (3.33) (3.72) (2) (0.65) (0.63) 0.1 0.95 ACL 0.892 0.914 0.924 0.87 0.72 LENGTH 151 198 120 77.5 52.8 (6.05) (9.97) (2.55) (0.83) (0.5) SYMM2 1.3 1.98 1.11 0.42 0.25 (0.41) (0.7) (0.47) (0.15) (-0.02) (2.9) (4.25) (2.3) (0.85) (0.74) # 모의실험4; n=500 mixbi distribution: quantile estimation with n=500 nboot=1000 n.sim=500 p=0.995 xi NCL NBPct NBBCa SBPct PBOne PBTwo 0.1 0.9 ACL 0.876 0.866 0.866 0.358 0.024 LENGTH 61.6 61.5 43.6 79.8 52.1 (2.32) (2.37) (0.87) (0.72) (0.43) SYMM2 1.48 1.53 1.06 -9.71 -3.91 (0.51) (0.52) (0.36) (-19.47) (-5.09) (3.54) (3.82) (2.16) (9.91) (-3.36) 0.1 0.95 ACL 0.892 0.918 0.912 0.584 0.05 LENGTH 66.3 84.8 54 98.3 62.4 (2.56) (3.68) (1.12) (0.91) (0.52) SYMM2 1.42 2.11 1.28 6.51 -5.33 (0.57) (0.84) (0.56) (-21.94) (-7.37) (3.34) (4.95) (2.43) (18.45) (-4.29) ####################################################################################################################################### > # n=300, qq=0.8; 예상 소요시간 약 80시간 > SimGEVnGLOnMixture(parameter="quantile",n=300,nboot=1000,n.sim=500,qq=0.8,xi.seq=c(0.1,0.2,0.3,0.4,0.5),dist="GEV") # 모의실험1: 예상소요시간 50시간 GEV distribution: quantile estimation with n=300 nboot=1000 n.sim=500 p=0.99 xi NCL NBPct NBBCa SBPct PBOne PBTwo 0.1 0.9 ACL 0.798 0.806 0.902 0.934 0.886 LENGTH 26.8 27.4 28.8 27.3 21.5 (0.61) (0.7) (0.42) (0.24) (0.18) SYMM2 0.71 0.85 0.88 0.82 0.95 (0.08) (0.1) (0.28) (0.39) (0.37) (1.85) (2.19) (1.81) (1.69) (2.25) 0.1 0.95 ACL 0.82 0.948 0.936 0.974 0.94 LENGTH 30.5 44.2 34.9 32.9 25.7 (0.75) (1.14) (0.53) (0.3) (0.21) SYMM2 0.69 1.73 1.01 0.96 1.07 (0.13) (0.74) (0.42) (0.53) (0.5) (1.7) (3.24) (1.89) (1.76) (2.2) 0.2 0.9 ACL 0.788 0.784 0.884 0.946 0.88 LENGTH 40.4 40.9 43.8 43.8 33.5 (0.98) (1.12) (0.66) (0.45) (0.32) SYMM2 0.77 0.81 0.89 0.92 0.94 (0.08) (0.08) (0.3) (0.44) (0.37) (1.86) (2.11) (1.84) (1.75) (2.29) 0.2 0.95 ACL 0.804 0.944 0.93 0.976 0.944 LENGTH 44.9 73.9 53.3 53.1 40 (1.09) (2.25) (0.83) (0.56) (0.38) SYMM2 0.73 1.98 1.09 1.09 1.12 (0.12) (0.76) (0.44) (0.6) (0.52) (1.66) (4.15) (1.97) (1.89) (2.47) 0.3 0.9 ACL 0.8 0.802 0.882 0.948 0.886 LENGTH 66.3 67.7 67.6 69.7 51.7 (1.66) (1.76) (1.06) (0.77) (0.53) SYMM2 0.89 0.96 0.9 1.12 1.2 (0.09) (0.11) (0.25) (0.49) (0.33) (2.21) (2.56) (1.85) (1.94) (2.71) 0.3 0.95 ACL 0.81 0.944 0.92 0.976 0.932 LENGTH 75 128 83 85.4 62 (2.13) (4.03) (1.35) (0.97) (0.66) SYMM2 0.88 2.47 1.13 1.34 1.33 (0.17) (0.93) (0.42) (0.65) (0.49) (1.93) (4.85) (2.1) (2.15) (2.64) 0.4 0.9 ACL 0.832 0.822 0.908 0.98 0.896 LENGTH 113 116 109 115 82.3 (3.51) (4.76) (1.91) (1.35) (0.91) SYMM2 0.89 0.89 0.99 1.32 1.38 (0.17) (0.18) (0.38) (0.7) (0.56) (2.53) (2.76) (2.14) (2.22) (3.12) 0.4 0.95 ACL 0.848 0.936 0.942 0.988 0.958 LENGTH 130 256 134 143 98.7 (5.59) (12.8) (2.43) (1.75) (1.1) SYMM2 0.86 2.67 1.22 1.58 1.57 (0.23) (1.05) (0.58) (0.93) (0.77) (2.28) (6.2) (2.33) (2.51) (3.17) 0.5 0.9 ACL 0.83 0.824 0.868 0.956 0.878 LENGTH 193 203 161 177 123 (9.51) (10.26) (3.11) (2.45) (1.56) SYMM2 1.04 1.11 0.82 1.19 1.18 (0.19) (0.21) (0.23) (0.59) (0.39) (2.48) (2.78) (1.83) (2.21) (2.81) 0.5 0.95 ACL 0.842 0.954 0.91 0.98 0.922 LENGTH 216 466 202 221 148 (10.29) (35.03) (4.08) (3.15) (1.87) SYMM2 1.02 2.82 1.12 1.51 1.34 (0.24) (1.11) (0.44) (0.84) (0.58) (2.37) (6.86) (2.15) (2.58) (2.85) > SimGEVnGLOnMixture(parameter="quantile",n=300,nboot=1000,n.sim=500,qq=0.8,xi.seq=c(0.4),dist="GLO") # 모의실험2: xi here is the parameter of GLO GLO distribution: quantile estimation with n=300 nboot=1000 n.sim=500 p=0.99 xi NCL NBPct NBBCa SBPct PBOne PBTwo 0.4 0.9 ACL 0.77 0.778 0.864 0.858 0.804 LENGTH 131 145 128 108 80 (4.22) (6.82) (2.51) (1.29) (0.9) SYMM2 0.76 0.9 0.79 0.66 0.61 (0.07) (0.09) (0.27) (0.25) (0.14) (2.2) (2.57) (1.92) (1.33) (1.62) 0.4 0.95 ACL 0.792 0.924 0.902 0.934 0.86 LENGTH 148 315 158 133 95.9 (4.79) (20.12) (3.24) (1.61) (1.07) SYMM2 0.81 2.39 1.02 0.87 0.78 (0.12) (1) (0.45) (0.43) (0.28) (2.11) (5.41) (2.25) (1.56) (1.78) > SimGEVnGLOnMixture(parameter="quantile",n=300,nboot=1000,n.sim=500,qq=0.8,xi.seq=c(0.1),dist="mixuni") # 모의실험3 mixuni distribution: quantile estimation with n=300 nboot=1000 n.sim=500 p=0.99 xi NCL NBPct NBBCa SBPct PBOne PBTwo 0.1 0.9 ACL 0.76 0.766 0.84 0.83 0.764 LENGTH 67.5 72.6 66.2 51.6 39.4 (2.22) (2.93) (1.35) (0.6) (0.43) SYMM2 0.72 0.83 0.8 0.51 0.46 (0.02) (0.03) (0.2) (0.12) (0.02) (2.01) (2.38) (1.91) (1.19) (1.37) 0.1 0.95 ACL 0.78 0.916 0.902 0.908 0.83 LENGTH 82.3 158 81.5 62.9 47.1 (4.07) (7.44) (1.73) (0.75) (0.52) SYMM2 0.77 2.53 1.07 0.69 0.63 (0.05) (0.91) (0.37) (0.26) (0.15) (1.92) (5.73) (2.2) (1.39) (1.49) > SimGEVnGLOnMixture(parameter="quantile",n=300,nboot=1000,n.sim=500,qq=0.8,xi.seq=c(0.1),dist="mixbi") # 모의실험4 mixbi distribution: quantile estimation with n=300 nboot=1000 n.sim=500 p=0.99 xi NCL NBPct NBBCa SBPct PBOne PBTwo 0.1 0.9 ACL 0.796 0.808 0.872 0.62 0.148 LENGTH 32.9 33.6 29.7 59.6 43.8 (1.06) (1.16) (0.6) (0.63) (0.43) SYMM2 0.85 0.91 0.92 4.72 -5.3 (0.13) (0.19) (0.24) (-13.88) (-8.08) (2) (2.25) (2.08) (14.86) (-3.97) 0.1 0.95 ACL 0.808 0.944 0.904 0.776 0.248 LENGTH 36.6 71.1 36.4 73.2 52.5 (1.24) (3.11) (0.77) (0.79) (0.52) SYMM2 0.84 2.4 1.1 7.5 -6.85 (0.16) (1.05) (0.38) (2.5) (-12.58) (1.87) (5.53) (2.26) (15.4) (-4.06)