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Table 1 Root-mean squared errors (RMSEs) in life expectancy at birth e0, percentage RMSEs in life expectancy in the open age interval e a (by method): by sex, level of life expectancy at birth, and open age interval (a+)

From: Expectation of life at old age: revisiting Horiuchi-Coale and reconciling with Mitra

    RMSE in e0 by method (years) Percentage RMSE in e a by method (percent)
Sex e0 range a Classical Extrapol. H.-C. H.-C. (hmd) Mitra Mitra (regr.) Classical Extrapol. H.-C. H.-C. (hmd) Mitra Mitra (regr.)
Female 40–50 55 0.75 6.60 0.40 0.41 0.47 0.46 8.05 73.76 4.54 4.64 5.33 5.22
Female 40–50 65 0.25 0.70 0.17 0.17 0.23 0.22 5.17 15.61 3.67 3.71 4.83 4.72
Female 40–50 75 0.06 0.16 0.05 0.05 0.05 0.05 3.40 8.42 2.78 2.85 2.93 2.88
Female 40–50 85 0.01 0.03 0.01 0.01 0.02 0.02 2.21 9.50 2.29 2.36 3.03 2.65
Female 50–60 55 1.53 10.23 0.57 0.54 0.38 0.48 11.86 81.82 4.54 4.31 3.14 3.90
Female 50–60 65 0.53 1.45 0.23 0.23 0.21 0.24 7.65 21.53 3.41 3.38 3.07 3.51
Female 50–60 75 0.12 0.25 0.07 0.08 0.08 0.08 4.54 12.93 2.82 2.85 2.73 2.89
Female 50–60 85 0.01 0.04 0.01 0.01 0.01 0.01 2.60 7.94 2.00 2.04 2.08 2.09
Female 60–70 55 3.57 18.78 0.79 0.77 0.43 0.57 21.21 114.15 4.63 4.59 2.52 3.34
Female 60–70 65 1.23 1.56 0.29 0.29 0.19 0.25 12.99 17.34 3.11 3.12 1.99 2.65
Female 60–70 75 0.25 0.29 0.09 0.09 0.06 0.09 6.55 9.15 2.54 2.53 1.77 2.30
Female 60–70 85 0.02 0.06 0.01 0.01 0.01 0.01 3.11 8.14 1.95 1.95 1.81 1.97
Female 70–80 55 5.38 3.32 1.36 1.19 0.99 1.08 24.14 15.00 5.99 5.29 4.53 4.93
Female 70–80 65 2.33 2.18 0.49 0.48 0.37 0.42 16.87 15.72 3.53 3.48 2.70 3.06
Female 70–80 75 0.67 0.56 0.16 0.15 0.11 0.13 10.10 8.25 2.56 2.35 1.75 2.14
Female 70–80 85 0.09 0.10 0.03 0.03 0.02 0.03 4.78 7.20 1.70 1.72 1.34 1.57
Female 80–90 55 8.08 23.67 1.90 1.61 0.96 1.17 28.64 81.77 6.86 5.81 3.50 4.22
Female 80–90 65 3.78 4.71 0.91 0.89 0.64 0.74 20.07 25.14 4.91 4.79 3.45 3.95
Female 80–90 75 1.42 2.11 0.34 0.27 0.20 0.27 13.80 20.10 3.35 2.72 2.04 2.60
Female 80–90 85 0.26 0.16 0.09 0.08 0.06 0.08 7.43 4.46 2.54 2.37 1.67 2.33
Male 40–50 55 0.71 3.47 0.26 0.24 0.20 0.24 8.26 45.83 3.27 3.07 2.59 3.01
Male 40–50 65 0.22 0.62 0.10 0.09 0.09 0.10 5.24 15.58 2.57 2.56 2.47 2.73
Male 40–50 75 0.04 0.09 0.02 0.02 0.02 0.02 3.05 7.71 2.05 2.04 1.89 2.12
Male 40–50 85 0.00 0.02 0.00 0.00 0.00 0.00 1.73 9.38 1.58 1.60 1.53 1.58
Male 50–60 55 1.49 4.23 0.46 0.43 0.32 0.39 12.30 34.85 4.03 3.80 2.71 3.38
Male 50–60 65 0.50 0.99 0.17 0.17 0.13 0.16 8.05 16.32 2.97 2.90 2.25 2.74
Male 50–60 75 0.10 0.18 0.05 0.05 0.04 0.05 4.65 9.42 2.56 2.51 2.13 2.51
Male 50–60 85 0.01 0.03 0.01 0.01 0.00 0.01 2.53 7.78 1.90 1.91 1.63 1.82
Male 60–70 55 2.45 2.76 0.55 0.58 0.47 0.48 15.32 17.23 3.49 3.71 3.00 3.06
Male 60–70 65 0.82 0.68 0.21 0.22 0.16 0.18 9.58 8.36 2.52 2.60 1.89 2.17
Male 60–70 75 0.17 0.20 0.06 0.06 0.05 0.06 5.43 7.20 2.07 2.12 1.63 1.92
Male 60–70 85 0.02 0.03 0.01 0.01 0.01 0.01 2.74 6.19 1.71 1.74 1.60 1.66
Male 70–80 55 5.34 3.02 1.30 1.06 0.66 0.77 24.10 13.85 6.00 4.95 3.17 3.62
Male 70–80 65 2.19 1.30 0.51 0.46 0.36 0.40 16.35 9.65 3.83 3.59 2.79 3.06
Male 70–80 75 0.66 0.53 0.16 0.13 0.11 0.13 10.44 8.39 2.66 2.23 1.81 2.09
Male 70–80 85 0.09 0.06 0.03 0.03 0.02 0.03 5.22 4.47 1.88 1.80 1.21 1.72
Total 40–50 55 11.01 9.56 1.91 1.75 0.65 1.00 41.98 36.36 7.34 6.73 2.48 3.82
Total 40–50 65 4.30 1.54 0.51 0.37 0.27 0.51 25.39 9.18 2.96 2.18 1.58 2.95
Total 40–50 75 1.06 1.97 0.33 0.25 0.19 0.22 12.10 21.67 3.82 2.90 2.24 2.51
Total 40–50 85 0.19 0.09 0.06 0.05 0.03 0.05 7.12 3.48 2.13 1.86 1.21 1.77
Total 50–60 55 0.72 4.80 0.33 0.31 0.32 0.34 8.09 57.95 3.83 3.76 3.89 4.02
Total 50–60 65 0.22 0.65 0.13 0.13 0.18 0.18 4.93 15.28 3.13 3.15 4.10 4.07
Total 50–60 75 0.05 0.09 0.03 0.03 0.03 0.03 3.05 6.24 2.24 2.27 2.14 2.28
Total 50–60 85 0.01 0.02 0.01 0.01 0.01 0.01 1.88 8.65 1.77 1.80 1.89 1.83
Total 60–70 55 1.47 5.74 0.48 0.45 0.30 0.39 11.81 47.86 4.00 3.78 2.53 3.26
Total 60–70 65 0.50 1.16 0.18 0.17 0.13 0.16 7.58 17.95 2.80 2.74 2.01 2.56
Total 60–70 75 0.10 0.16 0.05 0.05 0.05 0.06 4.26 7.56 2.40 2.40 2.22 2.43
Total 60–70 85 0.01 0.03 0.01 0.01 0.01 0.01 2.31 6.72 1.58 1.60 1.38 1.58
Total 70–80 55 3.12 3.93 0.66 0.62 0.48 0.54 18.72 25.25 4.01 3.79 2.96 3.29
Total 70–80 65 1.08 0.94 0.25 0.25 0.18 0.22 11.69 10.59 2.78 2.79 2.02 2.48
Total 70–80 75 0.23 0.23 0.08 0.08 0.06 0.07 6.32 6.88 2.35 2.36 1.81 2.16
Total 70–80 85 0.02 0.04 0.01 0.01 0.01 0.01 2.87 6.50 1.76 1.79 1.77 1.71
Total 80–90 55 4.54 2.52 1.21 1.06 0.77 0.82 20.94 11.87 5.47 4.87 3.72 3.86
Total 80–90 65 1.95 1.25 0.45 0.44 0.34 0.37 14.76 9.39 3.40 3.31 2.56 2.78
Total 80–90 75 0.59 0.53 0.15 0.13 0.10 0.12 9.36 8.21 2.40 2.15 1.63 1.97
Total 80–90 85 0.08 0.07 0.03 0.03 0.02 0.03 4.76 4.88 1.66 1.65 1.18 1.55
  1. e 0 life expectancy at birth, a starting age of the open age interval, Classical classical life table method, Extrapol. extrapolation of the death rates using the Gompertz model, H.-C. Horiuchi-Coale formula, H.-C. (hmd) Horiuchi-Coale formula with the Beta parameter re-estimated on the HMD data, Mitra Mitra formula, Mitra (regr.) Mitra formula with the mean population age in the open age interval substituted from the indirect estimate (6), RMSE root-mean squared estimation error, Percentage RMSE root-mean squared estimation errors as percent of values in corresponding full life tables from HMD (i.e., with a = 110)