Life Tables

Farhat Yusuf; Jo. M. Martins; David A. Swanson

doi:10.1007/978-94-007-6784-3_7

Methods of Demographic Analysis pp 143-172 | Cite as

Life Tables

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Farhat Yusuf
Jo. M. Martins
David A. Swanson

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First Online: 28 May 2013

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Abstract

The discussion of issues concerned with mortality, survival and longevity form an introduction to the estimation of life tables. Assumptions underlying the life table in regard to constancy of age-specific mortality rates, total number of births, and the absence of migration are discussed. This is followed by a detailed description and computational methods of the estimation of columns in the life table concerned with survivorship, deaths, person-years lived and life expectancy, in complete and abridged life tables. Interpretation and graphic representation of different life table columns is included. Basic data required for the construction of both a complete and an abridged life table are discussed, highlighting the differences between these two types of period life tables. Alternative methods of the building of life tables are considered and results compared. Step by step estimation of each component in life tables is indicated and numerical examples given. Apart from demographic uses of life tables, applications in other fields such as insurance, epidemiology and other commercial and industrial activities are discussed.

Keywords

Life Table Real Population Synthetic Population Hypothetical Population Average Annual Death Rate

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Appendices

Appendix 7.1: Input Data for Life Tables

Table A7.1

Deaths, population, m _x and q _x by age and sex for Australia

Age	Deaths, 2005–2007		Population, 2006		m _x		q _x
x	Males	Females	Males	Females	Males	Females	Males	Females
0	2,107	1,667	137,142	130,510	0.00039	0.00031	0.00506	0.00423
1	157	117	133,215	125,413	0.00027	0.00020	0.00027	0.00020
2	107	73	131,863	124,538	0.00016	0.00016	0.00016	0.00016
3	65	59	131,550	124,761	0.00016	0.00011	0.00016	0.00011
4	64	43	132,079	125,691	0.00039	0.00031	0.00039	0.00031
1–4	393	292	528,707	500,403	0.00025	0.00019	0.00125	0.00095
5	50	41	134,757	127,887	0.00012	0.00011	0.00012	0.00011
6	53	43	135,688	129,309	0.00013	0.00011	0.00013	0.00011
7	36	32	135,644	128,760	0.00009	0.00008	0.00009	0.00008
8	40	32	136,510	128,600	0.00010	0.00008	0.00010	0.00008
9	50	33	137,324	130,009	0.00012	0.00008	0.00012	0.00008
5–9	229	181	679,923	644,565	0.00011	0.00009	0.00055	0.00045
10	33	22	138,726	130,985	0.00008	0.00006	0.00008	0.00006
11	45	29	141,998	134,268	0.00011	0.0	0.00011	0.0
12	61	27	141,896	134,837	0.00014	0.0	0.00014	0.0
13	64	48	142,339	135,354	0.00015	0.00012	0.00015	0.00012
14	56	51	143,270	135,055	0.00013	0.00013	0.00013	0.00013
10–14	259	177	708,229	670,499	0.00012	0.00009	0.00060	0.00045
15	99	77	144,257	135,432	0.00023	0.00019	0.00023	0.00019
16	128	94	144,591	135,537	0.00030	0.00023	0.00030	0.00023
17	228	106	141,421	133,676	0.00054	0.00026	0.00054	0.00026
18	313	111	139,874	132,252	0.5	0.00028	0.5	0.00028
19	310	113	141,924	134,690	0.3	0.00028	0.3	0.00028
15–19	1,078	501	712,067	671,587	0.00050	0.00025	0.00250	0.00125
20	342	125	145,217	138,317	0.9	0.00030	0.9	0.00030
21	359	121	145,795	141,713	0.00082	0.00028	0.00082	0.00028
22	315	120	145,722	141,470	0.2	0.00028	0.2	0.00028
23	382	122	148,494	144,190	0.00086	0.00028	0.00086	0.00028
24	378	142	147,772	142,113	0.00085	0.00033	0.00085	0.00033
20–24	1,776	630	733,000	707,803	0.00081	0.00030	0.00404	0.00150
25	346	120	145,090	139,326	0.9	0.00029	0.9	0.00029
26	345	127	140,700	137,402	0.00082	0.00031	0.00082	0.00031
27	374	124	136,920	136,037	0.00091	0.00030	0.00091	0.00030
28	359	144	136,577	136,554	0.00088	0.00035	0.00088	0.00035
29	400	176	136,913	137,954	0.00097	0.00043	0.00097	0.00043
25–29	1,824	691	696,200	687,273	0.00087	0.00034	0.00434	0.00170
30	378	160	138,033	138,300	0.00091	0.00039	0.00091	0.00039
31	457	178	140,798	141,827	0.00108	0.00042	0.00108	0.00042
32	468	194	144,884	146,492	0.00108	0.00044	0.00108	0.00044
33	486	191	149,262	151,549	0.00109	0.00042	0.00109	0.00042
34	495	234	156,961	158,659	0.00105	0.00049	0.00105	0.00049
30–34	2,284	957	729,938	736,827	0.00104	0.00043	0.00519	0.00215
35	543	238	158,929	160,395	0.00114	0.00049	0.00114	0.00049
36	572	265	152,278	152,353	0.00125	0.00058	0.00125	0.00058
37	532	275	149,190	151,315	0.00119	0.00061	0.00119	0.00061
38	530	326	144,668	145,683	0.00122	0.5	0.00122	0.5
39	585	329	142,998	144,099	0.00136	0.6	0.00136	0.6
35–39	2,762	1,433	748,063	753,845	0.00123	0.00063	0.00613	0.00315
40	646	369	143,664	145,076	0.00150	0.00085	0.00150	0.00085
41	674	408	145,606	147,990	0.00154	0.00092	0.00154	0.00092
42	754	407	152,324	152,849	0.00165	0.00089	0.00165	0.00089
43	810	482	153,253	156,110	0.00176	0.00103	0.00176	0.00103
44	852	515	153,474	155,162	0.00185	0.00111	0.00185	0.00111
40–44	3,736	2,181	748,321	757,187	0.00166	0.00096	0.00827	0.00479
45	940	575	151,534	155,746	0.00207	0.00123	0.00207	0.00123
46	997	602	148,662	151,727	0.00224	0.00132	0.00224	0.00132
47	1,064	670	145,121	146,697	0.00244	0.00152	0.00244	0.00152
48	1,160	701	141,342	144,902	0.00274	0.00161	0.00274	0.00161
49	1,194	756	140,060	141,505	0.00284	0.00178	0.00284	0.00178
45–49	5,355	3,304	726,719	740,577	0.00246	0.00149	0.01222	0.00742
50	1,263	788	139,951	140,443	0.00301	0.00187	0.00301	0.00187
51	1,299	818	135,295	136,196	0.00320	0.00200	0.00319	0.00200
52	1,412	869	131,617	132,851	0.00358	0.00218	0.00357	0.00218
53	1,531	965	131,552	132,926	0.00388	0.00242	0.00387	0.00242
54	1,642	1,011	128,806	128,996	0.00425	0.00261	0.00424	0.00261
50–54	7,147	4,451	667,221	671,412	0.00357	0.00221	0.01769	0.01099
55	1,810	1,034	126,318	128,064	0.00478	0.00269	0.00477	0.00269
56	1,795	1,130	125,839	126,182	0.00475	0.00299	0.00474	0.00299
57	1,970	1,199	120,511	120,428	0.00545	0.00332	0.00544	0.00331
58	2,221	1,335	122,914	122,128	0.00602	0.00364	0.00600	0.00363
59	2,468	1,367	128,140	126,479	0.00642	0.00360	0.00640	0.00359
55–59	10,264	6,065	623,722	623,281	0.00549	0.00324	0.02708	0.01607
60	2,487	1,587	108,036	106,259	0.00767	0.00498	0.00764	0.00497
61	2,540	1,430	103,539	102,125	0.00818	0.00467	0.00815	0.00466
62	2,500	1,634	97,683	98,361	0.00853	0.00554	0.00849	0.00552
63	2,752	1,592	89,588	89,555	0.01024	0.00593	0.01019	0.00591
64	2,872	1,647	88,021	87,581	0.01088	0.00627	0.01082	0.00625
60–64	13,151	7,890	486,867	483,881	0.00900	0.00544	0.04401	0.02684
65	3,027	1,689	82,127	82,839	0.01229	0.00680	0.01221	0.00678
66	3,216	1,890	79,287	80,433	0.01352	0.00783	0.01343	0.00780
67	3,382	1,895	75,814	78,941	0.01487	0.00800	0.01476	0.00797
68	3,567	2,089	71,875	74,811	0.01654	0.00931	0.01640	0.00927
69	3,729	2,251	69,111	73,074	0.01799	0.01027	0.01783	0.01022
65–69	1,6921	9,814	378,214	390,098	0.01491	0.00839	0.07187	0.04109
70	3,825	2,332	66,313	69,944	0.01923	0.01111	0.01905	0.01105
71	3,991	2,553	61,145	66,218	0.02176	0.01285	0.02153	0.01277
72	4,257	2,704	58,941	63,666	0.02407	0.01416	0.02378	0.01406
73	4,559	2,956	57,185	62,892	0.02657	0.01567	0.02622	0.01555
74	5,048	3,401	55,513	61,449	0.03031	0.01845	0.02986	0.01828
70–74	21,680	13,946	299,097	324,169	0.02416	0.01434	0.11392	0.06922
75	5,554	3,711	55,271	62,549	0.03350	0.01978	0.03295	0.01959
76	6,059	4,145	53,469	61,965	0.03777	0.02230	0.03707	0.02205
77	6,430	4,534	49,760	59,520	0.04307	0.02539	0.04216	0.02507
78	6,805	5,089	47,596	58,196	0.04766	0.02915	0.04655	0.02873
79	7,046	5,444	44,296	55,629	0.05302	0.03262	0.05165	0.03210
75–79	31,894	22,923	250,392	297,859	0.04246	0.02565	0.19193	0.12052
80	7,255	6,019	40,960	53,834	0.05904	0.03727	0.05735	0.03659
81	7,345	6,551	36,590	51,571	0.06691	0.04234	0.06474	0.04146
82	7,335	7,109	32,686	47,593	0.07480	0.04979	0.07210	0.04858
83	7,426	7,401	28,931	44,291	0.08556	0.05570	0.08205	0.05419
84	7,339	7,973	25,918	41,305	0.09439	0.06434	0.09014	0.06233
80–84	36,700	35,053	165,085	238,594	0.07410	0.04897	0.31259	0.21814
85	6,930	8,128	22,212	37,638	0.10400	0.07198	0.09886	0.06948
86	6,295	7,971	18,884	32,957	0.11112	0.08062	0.10527	0.07750
87	5,643	7,834	13,723	25,681	0.13707	0.10168	0.12828	0.09676
88	4,925	7,602	11,052	22,456	0.14854	0.11284	0.13827	0.10681
89	4,548	7,339	9,453	20,088	0.16037	0.12178	0.14847	0.11479
85–89	28,341	38,874	75,324	138,820	0.12542	0.09334	0.47741	0.37840
90	4,168	7,373	7,658	17,495	0.18142	0.14048	0.16633	0.13126
91	3,676	7,100	6,058	15,240	0.20227	0.15529	0.18369	0.14410
92	3,103	6,624	4,628	12,245	0.22349	0.18032	0.20103	0.16541
93	2,440	5,705	3,379	9,330	0.24070	0.20382	0.21484	0.18497
94	1,898	4,752	2,352	7,279	0.26899	0.21761	0.23710	0.19626
90–94	15,285	31,554	24,075	61,589	0.21163	0.17078	0.69202	0.59841
95	1,452	3,924	1,667	5,390	0.29034	0.24267	0.25353	0.21641
96	1,086	3,118	1,165	3,946	0.31073	0.26339	0.26895	0.23274
97	728	2,369	684	2,691	0.35478	0.29345	0.30133	0.25590
98	490	1,792	475	1,868	0.34386	0.31977	0.29341	0.27569
99	326	1,268	331	1,209	0.32830	0.34960	0.28201	0.29758
95–99	4,082	12,471	4,322	15,104	0.31482	0.27523	0.88084	0.81522
100+	521	2,466	464	1,995	0.37428	0.41203	1.00000	1.00000

Sources: Australia (2008) for births; Australia (2009) for deaths, 2005–2007 and population, 2006

Notes: (1) Births, 2005–2007 were: 416,576 for males and 394,377 for females

(2) m _x $ =\displaystyle\frac{Deaths,2005-2007 }{3*Population,2006 } $. The q _x values were estimated by using Eq. (7.4) for ages 1–99 years, and Eq. (7.5) for age 0. The value of q ₁₀₀₊ was assumed to be 1 for both males and females. The underlined values refer to _n m _x and _n q _x estimated using Eqs. (7.1a) and (7.4a) respectively

Appendix 7.2: Complete Life Tables by Sex: Australia, 2005–2007

Table A7.2

Complete life table for Australian males, 2005–2007

x	$ {m_x} $	$ {q_x} $	${d_x} $	$ {l_x} $	$ {L_x} $	$ {T_x} $	$ {e_x} $
0	0.00512	0.00506	506	100,000	99,646	7,890,093	78.9
1	0.00039	0.00039	39	99,494	99,475	7,790,447	78.3
2	0.00027	0.00027	27	99,455	99,442	7,690,972	77.3
3	0.00016	0.00016	16	99,428	99,420	7,591,530	76.4
4	0.00016	0.00016	16	99,412	99,404	7,492,110	75.4
5	0.00012	0.00012	12	99,396	99,390	7,392,706	74.4
6	0.00013	0.00013	13	99,384	99,378	7,293,316	73.4
7	0.00009	0.00009	9	99,371	99,367	7,193,938	72.4
8	0.00010	0.00010	10	99,362	99,357	7,094,571	71.4
9	0.00012	0.00012	12	99,352	99,346	6,995,214	70.4
10	0.00008	0.00008	8	99,340	99,336	6,895,868	69.4
11	0.00011	0.00011	11	99,332	99,327	6,796,532	68.4
12	0.00014	0.00014	14	99,321	99,314	6,697,205	67.4
13	0.00015	0.00015	15	99,307	99,300	6,597,891	66.4
14	0.00013	0.00013	13	99,292	99,286	6,498,591	65.4
15	0.00023	0.00023	23	99,279	99,268	6,399,305	64.5
16	0.00030	0.00030	30	99,256	99,241	6,300,037	63.5
17	0.00054	0.00054	54	99,226	99,199	6,200,796	62.5
18	0.5	0.5	74	99,172	99,135	6,101,597	61.5
19	0.3	0.3	72	99,098	99,062	6,002,462	60.6
20	0.9	0.9	78	99,026	98,987	5,903,400	59.6
21	0.00082	0.00082	81	98,948	98,908	5,804,413	58.7
22	0.2	0.2	71	98,867	98,832	5,705,505	57.7
23	0.00086	0.00086	85	98,796	98,754	5,606,673	56.8
24	0.00085	0.00085	84	98,711	98,669	5,507,919	55.8
25	0.9	0.9	78	98,627	98,588	5,409,250	54.8
26	0.00082	0.00082	81	98,549	98,509	5,310,662	53.9
27	0.00091	0.00091	90	98,468	98,423	5,212,153	52.9
28	0.00088	0.00088	87	98,378	98,335	5,113,730	52.0
29	0.00097	0.00097	95	98,291	98,244	5,015,395	51.0
30	0.00091	0.00091	89	98,196	98,152	4,917,151	50.1
31	0.00108	0.00108	106	98,107	98,054	4,818,999	49.1
32	0.00108	0.00108	106	98,001	97,948	4,720,945	48.2
33	0.00109	0.00109	107	97,895	97,842	4,622,997	47.2
34	0.00105	0.00105	103	97,788	97,737	4,525,155	46.3
35	0.00114	0.00114	111	97,685	97,630	4,427,418	45.3
36	0.00125	0.00125	122	97,574	97,513	4,329,788	44.4
37	0.00119	0.00119	116	97,452	97,394	4,232,275	43.4
38	0.00122	0.00122	119	97,336	97,277	4,134,881	42.5
39	0.00136	0.00136	132	97,217	97,151	4,037,604	41.5
40	0.00150	0.00150	146	97,085	97,012	3,940,453	40.6
41	0.00154	0.00154	149	96,939	96,865	3,843,441	39.6
42	0.00165	0.00165	160	96,790	96,710	3,746,576	38.7
43	0.00176	0.00176	170	96,630	96,545	3,649,866	37.8
44	0.00185	0.00185	178	96,460	96,371	3,553,321	36.8
45	0.00207	0.00207	199	96,282	96,183	3,456,950	35.9
46	0.00224	0.00224	215	96,083	95,976	3,360,767	35.0
47	0.00244	0.00244	234	95,868	95,751	3,264,791	34.1
48	0.00274	0.00274	262	95,634	95,503	3,169,040	33.1
49	0.00284	0.00284	271	95,372	95,237	3,073,537	32.2
50	0.00301	0.00301	286	95,101	94,958	2,978,300	31.3
51	0.00320	0.00319	302	94,815	94,664	2,883,342	30.4
52	0.00358	0.00357	337	94,513	94,345	2,788,678	29.5
53	0.00388	0.00387	364	94,176	93,994	2,694,333	28.6
54	0.00425	0.00424	398	93,812	93,613	2,600,339	27.7
55	0.00478	0.00477	446	93,414	93,191	2,506,726	26.8
56	0.00475	0.00474	441	92,968	92,748	2,413,535	26.0
57	0.00545	0.00544	503	92,527	92,276	2,320,787	25.1
58	0.00602	0.00600	552	92,024	91,748	2,228,511	24.2
59	0.00642	0.00640	585	91,472	91,180	2,136,763	23.4
60	0.00767	0.00764	694	90,887	90,540	2,045,583	22.5
61	0.00818	0.00815	735	90,193	89,826	1,955,043	21.7
62	0.00853	0.00849	759	89,458	89,079	1,865,217	20.9
63	0.01024	0.01019	904	88,699	88,247	1,776,138	20.0
64	0.01088	0.01082	950	87,795	87,320	1,687,891	19.2
65	0.01229	0.01221	1,060	86,845	86,315	1,600,571	18.4
66	0.01352	0.01343	1,152	85,785	85,209	1,514,256	17.7
67	0.01487	0.01476	1,249	84,633	84,009	1,429,047	16.9
68	0.01654	0.01640	1,367	83,384	82,701	1,345,038	16.1
69	0.01799	0.01783	1,462	82,017	81,286	1,262,337	15.4
70	0.01923	0.01905	1,535	80,555	79,788	1,181,051	14.7
71	0.02176	0.02153	1,701	79,020	78,170	1,101,263	13.9
72	0.02407	0.02378	1,839	77,319	76,400	1,023,093	13.2
73	0.02657	0.02622	1,979	75,480	74,491	946,693	12.5
74	0.03031	0.02986	2,195	73,501	72,404	872,202	11.9
75	0.03350	0.03295	2,350	71,306	70,131	799,798	11.2
76	0.03777	0.03707	2,556	68,956	67,678	729,667	10.6
77	0.04307	0.04216	2,799	66,400	65,001	661,989	10.0
78	0.04766	0.04655	2,961	63,601	62,121	596,988	9.4
79	0.05302	0.05165	3,132	60,640	59,074	534,867	8.8
80	0.05904	0.05735	3,298	57,508	55,859	475,793	8.3
81	0.06691	0.06474	3,510	54,210	52,455	419,934	7.7
82	0.07480	0.07210	3,655	50,700	48,873	367,479	7.2
83	0.08556	0.08205	3,860	47,045	45,115	318,606	6.8
84	0.09439	0.09014	3,893	43,185	41,239	273,491	6.3
85	0.10400	0.09886	3,884	39,292	37,350	232,252	5.9
86	0.11112	0.10527	3,727	35,408	33,545	194,902	5.5
87	0.13707	0.12828	4,064	31,681	29,649	161,357	5.1
88	0.14854	0.13827	3,819	27,617	25,708	131,708	4.8
89	0.16037	0.14847	3,533	23,798	22,032	106,000	4.5
90	0.18142	0.16633	3,371	20,265	18,580	83,968	4.1
91	0.20227	0.18369	3,103	16,894	15,343	65,388	3.9
92	0.22349	0.20103	2,772	13,791	12,405	50,045	3.6
93	0.24070	0.21484	2,367	11,019	9,836	37,640	3.4
94	0.26899	0.23710	2,051	8,652	7,627	27,804	3.2
95	0.29034	0.25353	1,674	6,601	5,764	20,177	3.1
96	0.31073	0.26895	1,325	4,927	4,265	14,413	2.9
97	0.35478	0.30133	1,085	3,602	3,060	10,148	2.8
98	0.34386	0.29341	739	2,517	2,148	7,088	2.8
99	0.32830	0.28201	501	1,778	1,528	4,940	2.8
100+	0.37428	1.00000	1,277	1,277	3,412	3,412	2.7

Notes: (1) Values of m _x and q _x were copied from Table A7.1

(2) Values of the remaining five columns were estimated using Eqs. (7.8), (7.9), (7.12), (7.17) and (7.18) respectively for all ages except for L ₀ and L ₁₀₀₊ for which Eqs. (7.14) and (7.15) were used

Table A7.3

Complete life table for Australian females, 2005–2007

x	$ {m_x} $	$ {q_x} $	$ {d_x} $	$ {l_x} $	$ {L_x} $	$ {T_x} $	$ {e_x} $
0	0.00426	0.00423	423	100,000	99,704	8,358,643	83.6
1	0.00031	0.00031	31	99,577	99,562	8,258,939	82.9
2	0.00020	0.00020	20	99,546	99,536	8,159,377	82.0
3	0.00016	0.00016	16	99,526	99,518	8,059,841	81.0
4	0.00011	0.00011	11	99,510	99,505	7,960,323	80.0
5	0.00011	0.00011	11	99,499	99,494	7,860,818	79.0
6	0.00011	0.00011	11	99,488	99,483	7,761,324	78.0
7	0.00008	0.00008	8	99,477	99,473	7,661,841	77.0
8	0.00008	0.00008	8	99,469	99,465	7,562,368	76.0
9	0.00008	0.00008	8	99,461	99,457	7,462,903	75.0
10	0.00006	0.00006	6	99,453	99,450	7,363,446	74.0
11	0.0	0.0	7	99,447	99,444	7,263,996	73.0
12	0.0	0.0	7	99,440	99,437	7,164,552	72.0
13	0.00012	0.00012	12	99,433	99,427	7,065,115	71.1
14	0.00013	0.00013	13	99,421	99,415	6,965,688	70.1
15	0.00019	0.00019	19	99,408	99,399	6,866,273	69.1
16	0.00023	0.00023	23	99,389	99,378	6,766,874	68.1
17	0.00026	0.00026	26	99,366	99,353	6,667,496	67.1
18	0.00028	0.00028	28	99,340	99,326	6,568,143	66.1
19	0.00028	0.00028	28	99,312	99,298	6,468,817	65.1
20	0.00030	0.00030	30	99,284	99,269	6,369,519	64.2
21	0.00028	0.00028	28	99,254	99,240	6,270,250	63.2
22	0.00028	0.00028	28	99,226	99,212	6,171,010	62.2
23	0.00028	0.00028	28	99,198	99,184	6,071,798	61.2
24	0.00033	0.00033	33	99,170	99,154	5,972,614	60.2
25	0.00029	0.00029	29	99,137	99,123	5,873,460	59.2
26	0.00031	0.00031	31	99,108	99,093	5,774,337	58.3
27	0.00030	0.00030	30	99,077	99,062	5,675,244	57.3
28	0.00035	0.00035	35	99,047	99,030	5,576,182	56.3
29	0.00043	0.00043	43	99,012	98,991	5,477,152	55.3
30	0.00039	0.00039	39	98,969	98,950	5,378,161	54.3
31	0.00042	0.00042	42	98,930	98,909	5,279,211	53.4
32	0.00044	0.00044	44	98,888	98,866	5,180,302	52.4
33	0.00042	0.00042	42	98,844	98,823	5,081,436	51.4
34	0.00049	0.00049	48	98,802	98,778	4,982,613	50.4
35	0.00049	0.00049	48	98,754	98,730	4,883,835	49.5
36	0.00058	0.00058	57	98,706	98,678	4,785,105	48.5
37	0.00061	0.00061	60	98,649	98,619	4,686,427	47.5
38	0.5	0.5	74	98,589	98,552	4,587,808	46.5
39	0.6	0.6	75	98,515	98,478	4,489,256	45.6
40	0.00085	0.00085	84	98,440	98,398	4,390,778	44.6
41	0.00092	0.00092	90	98,356	98,311	4,292,380	43.6
42	0.00089	0.00089	87	98,266	98,223	4,194,069	42.7
43	0.00103	0.00103	101	98,179	98,129	4,095,846	41.7
44	0.00111	0.00111	109	98,078	98,024	3,997,717	40.8
45	0.00123	0.00123	121	97,969	97,909	3,899,693	39.8
46	0.00132	0.00132	129	97,848	97,784	3,801,784	38.9
47	0.00152	0.00152	149	97,719	97,645	3,704,000	37.9
48	0.00161	0.00161	157	97,570	97,492	3,606,355	37.0
49	0.00178	0.00178	173	97,413	97,327	3,508,863	36.0
50	0.00187	0.00187	182	97,240	97,149	3,411,536	35.1
51	0.00200	0.00200	194	97,058	96,961	3,314,387	34.1
52	0.00218	0.00218	211	96,864	96,759	3,217,426	33.2
53	0.00242	0.00242	234	96,653	96,536	3,120,667	32.3
54	0.00261	0.00261	252	96,419	96,293	3,024,131	31.4
55	0.00269	0.00269	259	96,167	96,038	2,927,838	30.4
56	0.00299	0.00299	287	95,908	95,765	2,831,800	29.5
57	0.00332	0.00331	317	95,621	95,463	2,736,035	28.6
58	0.00364	0.00363	346	95,304	95,131	2,640,572	27.7
59	0.00360	0.00359	341	94,958	94,788	2,545,441	26.8
60	0.00498	0.00497	470	94,617	94,382	2,450,653	25.9
61	0.00467	0.00466	439	94,147	93,928	2,356,271	25.0
62	0.00554	0.00552	517	93,708	93,450	2,262,343	24.1
63	0.00593	0.00591	551	93,191	92,916	2,168,893	23.3
64	0.00627	0.00625	579	92,640	92,351	2,075,977	22.4
65	0.00680	0.00678	624	92,061	91,749	1,983,626	21.5
66	0.00783	0.00780	713	91,437	91,081	1,891,877	20.7
67	0.00800	0.00797	723	90,724	90,363	1,800,796	19.8
68	0.00931	0.00927	834	90,001	89,584	1,710,433	19.0
69	0.01027	0.01022	911	89,167	88,712	1,620,849	18.2
70	0.01111	0.01105	975	88,256	87,769	1,532,137	17.4
71	0.01285	0.01277	1,115	87,281	86,724	1,444,368	16.5
72	0.01416	0.01406	1,211	86,166	85,561	1,357,644	15.8
73	0.01567	0.01555	1,321	84,955	84,295	1,272,083	15.0
74	0.01845	0.01828	1,529	83,634	82,870	1,187,788	14.2
75	0.01978	0.01959	1,608	82,105	81,301	1,104,918	13.5
76	0.02230	0.02205	1,775	80,497	79,610	1,023,617	12.7
77	0.02539	0.02507	1,974	78,722	77,735	944,007	12.0
78	0.02915	0.02873	2,205	76,748	75,646	866,272	11.3
79	0.03262	0.03210	2,393	74,543	73,347	790,626	10.6
80	0.03727	0.03659	2,640	72,150	70,830	717,279	9.9
81	0.04234	0.04146	2,882	69,510	68,069	646,449	9.3
82	0.04979	0.04858	3,237	66,628	65,010	578,380	8.7
83	0.05570	0.05419	3,435	63,391	61,674	513,370	8.1
84	0.06434	0.06233	3,737	59,956	58,088	451,696	7.5
85	0.07198	0.06948	3,906	56,219	54,266	393,608	7.0
86	0.08062	0.07750	4,054	52,313	50,286	339,342	6.5
87	0.10168	0.09676	4,670	48,259	45,924	289,056	6.0
88	0.11284	0.10681	4,656	43,589	41,261	243,132	5.6
89	0.12178	0.11479	4,469	38,933	36,699	201,871	5.2
90	0.14048	0.13126	4,524	34,464	32,202	165,172	4.8
91	0.15529	0.14410	4,314	29,940	27,783	132,970	4.4
92	0.18032	0.16541	4,239	25,626	23,507	105,187	4.1
93	0.20382	0.18497	3,956	21,387	19,409	81,680	3.8
94	0.21761	0.19626	3,421	17,431	15,721	62,271	3.6
95	0.24267	0.21641	3,032	14,010	12,494	46,550	3.3
96	0.26339	0.23274	2,555	10,978	9,701	34,056	3.1
97	0.29345	0.25590	2,155	8,423	7,346	24,355	2.9
98	0.31977	0.27569	1,728	6,268	5,404	17,009	2.7
99	0.34960	0.29758	1,351	4,540	3,865	11,605	2.6
100+	0.41203	1.00000	3,189	3,189	7,740	7,740	2.4

Notes: (1) Values of m _x and q _x were copied from Table A7.1

(2) Values of the remaining five columns were estimated using Eqs. (7.8), (7.9), (7.12), (7.17) and (7.18) respectively for all ages except for L ₀ and L ₁₀₀₊ for which Eqs. (7.14) and (7.15) were used

Appendix 7.3: Abridged Life Tables by Sex: Australia, 2005–2007

Table A7.4

Abridged life table for Australian males, 2005–2007

x	n	_n m _x	_n q _x	_n d _x	l _x	_n L _x	T _x	e _x
0	1	0.00512	0.00506	506	100,000	99,646	7,892,971	78.9
1	4	0.00025	0.00100	99	99,494	397,778	7,793,325	78.3
5	5	0.00011	0.00055	55	99,395	496,838	7,395,547	74.4
10	5	0.00012	0.00060	60	99,340	496,550	6,898,709	69.4
15	5	0.00050	0.00250	248	99,280	495,780	6,402,159	64.5
20	5	0.00081	0.00404	400	99,032	494,160	5,906,379	59.6
25	5	0.00087	0.00434	428	98,632	492,090	5,412,219	54.9
30	5	0.00104	0.00519	510	98,204	489,745	4,920,129	50.1
35	5	0.00123	0.00613	599	97,694	486,973	4,430,384	45.3
40	5	0.00166	0.00827	803	97,095	483,468	3,943,411	40.6
45	5	0.00246	0.01222	1,177	96,292	478,518	3,459,943	35.9
50	5	0.00357	0.01769	1,683	95,115	471,368	2,981,425	31.3
55	5	0.00549	0.02708	2,530	93,432	460,835	2,510,057	26.9
60	5	0.00900	0.04401	4,001	90,902	444,508	2,049,222	22.5
65	5	0.01491	0.07187	6,246	86,901	418,890	1,604,714	18.5
70	5	0.02416	0.11392	9,188	80,655	380,305	1,185,824	14.7
75	5	0.04246	0.19193	13,717	71,467	323,043	805,519	11.3
80	5	0.07410	0.31259	18,052	57,750	243,620	482,476	8.4
85	5	0.12542	0.47741	18,952	39,698	151,110	238,856	6.0
90	5	0.21163	0.69202	14,357	20,746	67,838	87,746	4.2
95	5	0.31482	0.88084	5,628	6,389	17,875	19,908	3.1
100+	5+	0.37428	1.00000	761	761	2,033	2,033	2.7

Note: In the above table x refers to the beginning of an age interval and n its width. Values of _n m _x and _n q _x were copied from Table A7.1. The remaining five columns were estimated using Eqs. (7.8a), (7.9a), (7.12a), (7.17) and (7.18). Eq. (7.15) was used for the estimation of L ₁₀₀₊

Table A7.5

Abridged life table for Australian females, 2005–2007

x	n	_n m _x	_n q _x	_n d _x	l _x	_n L _x	T _x	e _x
0	1	0.00426	0.00423	423	100,000	99,704	8,360,108	83.6
1	4	0.00019	0.6	76	99,577	398,156	8,260,404	83.0
5	5	0.00009	0.00045	45	99,501	497,393	7,862,248	79.0
10	5	0.00009	0.00045	45	99,456	497,168	7,364,855	74.1
15	5	0.00025	0.00125	124	99,411	496,745	6,867,687	69.1
20	5	0.00030	0.00150	149	99,287	496,063	6,370,942	64.2
25	5	0.00034	0.00170	169	99,138	495,268	5,874,879	59.3
30	5	0.00043	0.00215	213	98,969	494,313	5,379,611	54.4
35	5	0.00063	0.00315	311	98,756	493,003	4,885,298	49.5
40	5	0.00096	0.00479	472	98,445	491,045	4,392,295	44.6
45	5	0.00149	0.00742	727	97,973	488,048	3,901,250	39.8
50	5	0.00221	0.01099	1,069	97,246	483,558	3,413,202	35.1
55	5	0.00324	0.01607	1,546	96,177	477,020	2,929,644	30.5
60	5	0.00544	0.02684	2,540	94,631	466,805	2,452,624	25.9
65	5	0.00839	0.04109	3,784	92,091	450,995	1,985,819	21.6
70	5	0.01434	0.06922	6,113	88,307	426,253	1,534,824	17.4
75	5	0.02565	0.12052	9,906	82,194	386,205	1,108,571	13.5
80	5	0.04897	0.21814	15,769	72,288	322,018	722,366	10.0
85	5	0.09334	0.37840	21,387	56,519	229,128	400,348	7.1
90	5	0.17078	0.59841	21,023	35,132	123,103	171,220	4.9
95	5	0.27523	0.81522	11,502	14,109	41,790	48,117	3.4
100+	5+	0.41203	1.00000	2,607	2,607	6,327	6,327	2.4

Note: In the above table x refers to the beginning of an age interval and n its width. Values of _n m _x and _n q _x were copied from Table A7.1. The remaining five columns were estimated using Eqs. (7.8a), (7.9a), (7.12a), (7.17) and (7.18). Eq. (7.15) was used for the estimation of L ₁₀₀₊

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Authors and Affiliations

Farhat Yusuf
- 1
- 2
Jo. M. Martins
- 2
David A. Swanson
- 3

1.Menzies Centre for Health Policy Sydney School of Public HealthThe University of SydneySydneyAustralia
2.Department of Marketing and Management Faculty of Business and EconomicsMacquarie UniversityNorth RydeAustralia
3.Department of Sociology College of Humanities, Arts and Social SciencesUniversity of California RiversideRiversideUSA

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