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

Ediev, Dalkhat M.

doi:10.1186/s41118-018-0029-7

Genus

Journal of Population Sciences

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

e₀ 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)

Back to article page