The concept of the Equivalent Length of Life for quantifying differences in age-at-death distributions across countries

Table 1 Mean and variance (S ²) of the summary measures of the life-table age-at-death distributions (e ₁₀, e _C, e _A) and mean, variance and covariance of its components (dispersion SD, and skewness A’) across 35 developed countries, by sex. Selected years between 1970 and 2010, and absolute change in the statistics in two sub-periods: 1970–2005 and 2005–2010

Statistic	1970	1980	1990	2000	2005	2010^a	1970–2005	2005–2010
Women
Mean(e ₁₀)	65.7	67.0	68.3	69.7	70.6	71.6	4.9	1.0
Mean(e _C)	52.4	53.8	55.2	56.8	57.8	59.0	5.4	1.2
Mean(e _A)	48.9	50.3	51.6	53.1	54.2	55.3	5.3	1.1
Mean(SD)	13.3	13.2	13.1	12.9	12.7	12.6	−0.7	−0.1
Mean(A)	−0.27	−0.27	−0.27	−0.28	−0.29	−0.29	−0.02	0.00
S ²(e ₁₀)	1.43	3.04	4.49	7.44	8.94	7.37	7.51	−1.57
S ²(e _C)	2.04	3.99	5.95	10.80	13.83	11.34	11.79	−2.49
S ²(e _A)	2.19	4.09	5.66	10.82	14.22	11.76	12.04	−2.46
S ²(SD)	0.43	0.41	0.30	0.50	0.74	0.63	0.31	−0.11
S ²(A’)	0.04	0.07	0.06	0.08	0.07	0.07	0.03	0.00
cor (e ₁₀,SD)	−0.11	−0.25	−0.50	−0.74	−0.80	−0.77	−0.69	0.03
cor (SD,A’)	−0.54	−0.38	−0.06	−0.31	−0.49	−0.48	0.05	0.01
cor (e ₁₀,A’)	−0.11	−0.10	−0.36	−0.11	0.06	0.11	0.16	0.05
Men
Mean(e ₁₀)	59.5	60.0	61.2	62.7	63.8	65.3	4.3	1.5
Mean(e _C)	44.5	45.1	46.3	48.0	49.4	51.0	4.9	1.6
Mean(e _A)	41.0	41.7	42.8	44.5	46.0	47.5	5.0	1.5
Mean(SD)	15.0	14.9	14.9	14.7	14.4	14.3	−0.6	−0.1
Mean(A)	−0.23	−0.23	−0.23	−0.24	−0.24	−0.25	−0.01	−0.01
S ²(e ₁₀)	3.11	7.22	11.13	22.58	29.28	23.27	26.17	−6.01
S ²(e _C)	5.89	12.61	16.96	32.95	42.28	34.17	36.39	−8.21
S ²(e _A)	6.37	12.22	15.34	27.16	34.55	28.46	28.18	−6.09
S ²(SD)	4.97	5.45	4.94	5.48	7.72	7.10	2.75	−0.62
S ²(A’)	0.16	0.15	0.25	0.46	0.93	0.86	0.77	−0.07
cor (e ₁₀,SD)	−0.74	−1.03	−1.39	−3.47	−7.35	−6.56	−6.61	0.78
cor (SD,A’)	−0,60	−0.16	−0.04	0.52	0.61	0.58	1.21	−0.03
cor (e ₁₀,A’)	0.03	−0.36	−0.59	−0.86	−0.90	−0.86	−0.93	0.04

Notes: the table shows variance in statistics of the distribution of life-table ages at death above age 10; e ₁₀ is the life expectancy at age 10; e _C is the Equivalent Length of Life with e ₁₀ adjusted for dispersion of ages at death above age 10; e _A is the Equivalent Length of Life with e ₁₀ adjusted for dispersion and skewness of ages at death above age 10; SD is the standard deviation; A and A’ are the skewness statistics; cor stands for correlation. The statistics of the life-table age-at-death distribution above age 10 for the individual countries, by sex, and selected years, can be viewed from the Appendix (Table 3 and Fig. 2). Source: Authors’ estimations based on Human Mortality Database (2014)
^aOr latest available year