294:
the incidence of these events in the recent past, and sometimes developing expectations of how these past events will change over time (for example, whether the progressive reductions in mortality rates in the past will continue) and deriving expected rates of such events in the future, usually based on the age or other relevant characteristics of the population. An actuary's job is to form a comparison between people at risk of death and people who actually died to come up with a probability of death for a person at each age number, defined as qx in an equation. When analyzing a population, one of the main sources used to gather the required information is insurance by obtaining individual records that belong to a specific population. These are called mortality tables if they show death rates, and morbidity tables if they show various types of sickness or disability rates.
134:
218:, and safety standards that did not exist in the early years of this cohort. A life table is created by mortality rates and census figures from a certain population, ideally under a closed demographic system. This means that immigration and emigration do not exist when analyzing a cohort. A closed demographic system assumes that migration flows are random and not significant, and that immigrants from other populations have the same risk of death as an individual from the new population. Another benefit from mortality tables is that they can be used to make predictions on demographics or different populations.
307:
146:
20:
298:
and to factor in a range of non-traditional behaviors (e.g. gambling, debt load) into specialized calculations utilized by some institutions for evaluating risk. This is particularly the case in non-life insurance (e.g. the pricing of motor insurance can allow for a large number of risk factors, which requires a correspondingly complex table of expected claim rates). However the expression "life table" normally refers to human survival rates and is not relevant to non-life insurance.
71:
life table is more frequently used because it is able to make a prediction of any expected changes in the mortality rates of a population in the future. This type of table also analyzes patterns in mortality rates that can be observed over time. Both of these types of life tables are created based on
1609:
are the most commonly mathematical used devices. The latter includes information on health in addition to mortality. By watching over the life expectancy of any year(s) being studied, epidemiologists can see if diseases are contributing to the overall increase in mortality rates. Epidemiologists are
293:
products, and ensure the solvency of insurance companies through adequate reserves, actuaries must develop projections of future insured events (such as death, sickness, and disability). To do this, actuaries develop mathematical models of the rates and timing of the events. They do this by studying
213:
Life tables can be constructed using projections of future mortality rates, but more often they are a snapshot of age-specific mortality rates in the recent past, and do not necessarily purport to be projections. For these reasons, the older ages represented in a life table may have a greater chance
221:
However, there are also weaknesses of the information displayed on life tables. One being that they do not state the overall health of the population. There is more than one disease present in the world, and a person can have more than one disease at different stages simultaneously, introducing the
297:
The availability of computers and the proliferation of data gathering about individuals has made possible calculations that are more voluminous and intensive than those used in the past (i.e. they crunch more numbers) and it is more common to attempt to provide different tables for different uses,
75:
Other life tables in historical demography may be based on historical records, although these often undercount infants and understate infant mortality, on comparison with other regions with better records, and on mathematical adjustments for varying mortality levels and life expectancies at birth.
72:
an actual population from the present, as well as an educated prediction of the experience of a population in the near future. In order to find the true life expectancy average, 100 years would need to pass and by then finding that data would be of no use as healthcare is continually advancing.
66:
There are two types of life tables used in actuarial science. The period life table represents mortality rates during a specific time period for a certain population. A cohort life table, often referred to as a generation life table, is used to represent the overall mortality rates of a certain
280:
Life tables that relate to maternal deaths and infant moralities are important, as they help form family planning programs that work with particular populations. They also help compare a country's average life expectancy with other countries. Comparing life expectancy globally helps countries
1573:
In practice, it is useful to have an ultimate age associated with a mortality table. Once the ultimate age is reached, the mortality rate is assumed to be 1.000. This age may be the point at which life insurance benefits are paid to a survivor or annuity payments cease.
197:
and environment does not change. If a population were to have a constant number of people each year, it would mean that the probabilities of death from the life table were completely accurate. Also, an exact number of 100,000 people were born each year with no
1544:
Further descriptions: The variable dx stands for the number of deaths that would occur within two consecutive age numbers. An example of this is the number of deaths in a cohort that were recorded between the age of seven and the age of eight. The variable
1464:
1001:
1591:
The Less-Than-One Method: This is a variation on the Forced Method. The ultimate mortality rate is set equal to the expected mortality at a selected ultimate age, rather 1.000 as in the Forced Method. This rate will be less than
1581:
The Forced Method: Select an ultimate age and set the mortality rate at that age equal to 1.000 without any changes to other mortality rates. This creates a discontinuity at the ultimate age compared to the penultimate and prior
752:
1996:
1191:
814:
1316:
120:
All mortality tables are specific to environmental and life circumstances, and are used to probabilistically determine expected maximum age within those environmental conditions.
1239:
268:(also known as the Sullivan method) are based on external information on the proportion in each state. Life tables can also be extended to show life expectancies in different
243:
Life tables can be extended to include other information in addition to mortality, for instance health information to calculate health expectancy. Health expectancies such as
551:
1043:
1605:
and public health, both standard life tables (used to calculate life expectancy), as well as the
Sullivan and multi-state life tables (used to calculate health expectancy)
646:
584:
1536:
847:
498:
441:
411:
354:
1115:
1907:
2173:
1305:
1284:
1263:
1088:
1067:
871:
608:
465:
378:
882:
193:
individuals assuming a stationary population with overlapping generations. "Static life tables" and "cohort life tables" will be identical if population is in
1610:
able to help demographers understand the sudden decline of life expectancy by linking it to the health problems that are arising in certain populations.
281:
understand why one country's life expectancy is rising substantially by looking at each other's healthcare, and adopting ideas to their own systems.
229:
The life table observes the mortality experience of a single generation, consisting of 100,000 births, at every age number they can live through.
1975:
659:
1685:
1541:
This symbol refers to central rate of mortality. It is approximately equal to the average force of mortality, averaged over the year of age.
210:
life tables, as cohort life tables can only be constructed using data up to the current point, and distant projections for future mortality.
1585:
The
Blended Method: Select an ultimate age and blend the rates from some earlier age to dovetail smoothly into 1.000 at the ultimate age.
214:
of not being representative of what lives at these ages may experience in future, as it is predicated on current advances in medicine,
139:
U.S. Social
Security Administration (SSA) "Actuarial life table" allows study of life expectancy as a function of age already achieved.
47:) is a table which shows, for each age, the probability that a person of that age will die before their next birthday ("probability of
1749:"Life expectancy as a summary of mortality in a population: statistical considerations and suitability for use by health authorities"
1588:
The
Pattern Method: Let the pattern of mortality continue until the rate approaches or hits 1.000 and set that as the ultimate age.
1957:
2163:
1126:
2158:
262:(also known as increment-decrements life tables) are based on transition rates in and out of the different states and to death
1629:
758:
1824:
55:
of people from a certain population. They can also be explained as a long-term mathematical way to measure a population's
2193:
133:
185:
show the probability of death of people from a given cohort (especially birth year) over the course of their lifetime.
2075:
2041:
2128:
2218:
1844:
107:
1459:{\displaystyle \,{}_{t\mid k}q_{x}={}_{t}p_{x}\cdot {}_{k}q_{x+t}={\ell _{x+t}-\ell _{x+t+k} \over \ell _{x}}}
232:
Life tables are usually constructed separately for men and for women because of their substantially different
110:. It examines the mortality rates of all the people who have Social Security to decide which actions to take.
244:
114:
1619:
251:
are the remaining number of years a person can expect to live in a specific health state, such as free of
1201:
2223:
2208:
67:
population's entire lifetime. They must have had to be born during the same specific time interval. A
509:
255:. Two types of life tables are used to divide the life expectancy into life spent in various states:
1655:
1011:
623:
561:
306:
226:. Therefore, life tables also do not show the direct correlation of mortality and morbidity.
2168:
1513:
824:
470:
418:
383:
331:
2183:
1722:
1093:
996:{\displaystyle \,d_{x}=\ell _{x}-\ell _{x+1}=\ell _{x}\cdot (1-p_{x})=\ell _{x}\cdot q_{x}}
145:
8:
2213:
1289:
1268:
1247:
1072:
1051:
855:
592:
449:
362:
190:
176:
show the current probability of death (for people of different ages, in the current year)
68:
1961:
1781:
1748:
1482:
248:
1872:
Barendregt, Jan J (September 2009). "Coping with multiple morbidity in a life table".
1561:
stands for the years lived beyond each age number x by all members in the generation.
2092:
2071:
2037:
2004:
1889:
1786:
1768:
1634:
52:
28:
321:
chart from Table 1. Life table for the total population: United States, 2003, Page 8
2095:
1881:
1776:
1760:
2134:
194:
2051:
1624:
1553:, represents the number of people who lived between two consecutive age numbers.
237:
236:. Other characteristics can also be used to distinguish different risks, such as
155:
life expectancy—the number of years of life expected beyond subject's current age
91:
2152:
19:
1820:
273:
233:
2178:
1885:
2202:
2113:
2008:
1933:
1772:
1565:
represents the life expectancy for members already at a specific age number.
215:
1893:
1790:
1602:
747:{\displaystyle \,\ell _{x+1}=\ell _{x}\cdot (1-q_{x})=\ell _{x}\cdot p_{x}}
103:
1764:
269:
223:
199:
84:
60:
252:
203:
32:
2065:
1490:, i.e. the number of people dying in a short interval starting at age
2099:
1823:. U.S. Social Security Administration Office of Chief Actuary. 2020.
290:
56:
1723:"LIFE TABLES FOR THE UNITED STATES SOCIAL SECURITY AREA 1900–2100"
99:
79:
From this starting point, a number of inferences can be derived.
2123:
2146:
2066:
Preston, Samuel H.; Patrick
Heuveline; Michel Guillot (2001).
2179:
Actuarial Life Table from the U.S. Social
Security department
2140:
1997:"U.S. life expectancy declines for the first time since 1993"
617:
48:
2118:
1186:{\displaystyle \,{}_{t}p_{x}={\ell _{x+t} \over \ell _{x}}}
1747:
Silcocks, P. B. S.; Jenner, D. A.; Reza, R. (2001-01-01).
1845:"Introducing Migratory Flows in Life Table Construction"
2068:
Demography: measuring and modeling population processes
2031:
1690:
Sociology
Discussion - Discuss Anything About Sociology
2188:
2174:
UK Government
Actuary Department's Interim Life Tables
16:
Table which shows probability of death at various ages
1516:
1319:
1292:
1271:
1250:
1204:
1129:
1096:
1075:
1054:
1014:
885:
858:
827:
809:{\displaystyle \,{\ell _{x+1} \over \ell _{x}}=p_{x}}
761:
662:
626:
595:
564:
512:
473:
452:
421:
386:
365:
334:
325:
The basic algebra used in life tables is as follows.
59:. Tables have been created by demographers including
1746:
1577:Four methods can be used to end mortality tables:
1530:
1458:
1299:
1278:
1257:
1233:
1185:
1109:
1082:
1061:
1037:
995:
865:
841:
808:
746:
640:
602:
578:
545:
492:
459:
435:
405:
372:
348:
2200:
1908:"Life-tables and their demographic applications"
1807:, Cambridge University Press, 2013, pp. 104–118.
1503:and also divided by the length of the interval.
1486:, i.e. the instantaneous mortality rate at age
1815:
1813:
1753:Journal of Epidemiology & Community Health
2159:UN Model Life Tables for Developing Countries
240:status, occupation, and socioeconomic class.
2036:. Ohio: Glencoe McGraw–Hill. pp. A-22.
1838:
1836:
1834:
1810:
1686:"Life Table: Meaning, Types and Importance"
1568:
206:involved. "Life table" primarily refers to
63:, Reed and Merrell, Keyfitz, and Greville.
1871:
1557:of zero is equal to 100,000. The variable
1286:more years, then die within the following
1244:the probability that someone aged exactly
1048:the probability that someone aged exactly
446:the probability that someone aged exactly
359:the probability that someone aged exactly
2169:WHO-Global Health Observatory Life Tables
2054:. Office of the State Actuary. 2008-09-22
1994:
1780:
1517:
1320:
1293:
1272:
1251:
1205:
1130:
1097:
1090:more years, i.e. live up to at least age
1076:
1055:
1015:
886:
859:
828:
762:
663:
627:
596:
565:
513:
474:
453:
422:
387:
366:
335:
284:
98:Life tables are also used extensively in
1831:
589:the number of people who survive to age
305:
23:2003 US mortality table, Table 1, Page 1
18:
2147:Latin American Human Mortality Database
2032:Shepard, Jon; Robert W. Greene (2003).
87:of surviving any particular year of age
2201:
51:"). In other words, it represents the
2194:World Health Organisation Life Tables
2091:
1990:
1988:
1931:
1680:
1678:
1676:
1647:
151:SSA life table data, plotted to show
113:The concept is also of importance in
1716:
1714:
1712:
1710:
1708:
1706:
162:There are two types of life tables:
2129:Australian Human Mortality Database
1549:, which stands for the opposite of
1234:{\displaystyle \,{}_{t\mid k}q_{x}}
13:
2085:
1985:
1827:from the original on July 8, 2023.
1673:
1653:
852:the number of people who die aged
301:
14:
2235:
2153:Latin American Mortality Database
2124:Canadian Human Mortality Database
2107:
1842:
1703:
1630:Gompertz–Makeham law of mortality
648:lives, typically taken as 100,000
106:. An area that uses this tool is
2141:United States Mortality Database
1720:
144:
132:
2184:US CDC Vital Statistics Reports
2135:The Japanese Mortality Database
1995:Bernstein, Lenny (2016-12-08).
1968:
1950:
1925:
1874:Mathematical Population Studies
1596:
546:{\displaystyle \,p_{x}=1-q_{x}}
1900:
1865:
1797:
1740:
964:
945:
715:
696:
487:
475:
400:
388:
1:
2164:UN Extended Model Life Tables
2025:
1960:. avon.nhs.uk. Archived from
1958:"Period Abridged Life Tables"
1805:The Demography of Roman Italy
1038:{\displaystyle \,{}_{t}p_{x}}
380:will die before reaching age
245:disability-adjusted life year
123:
115:product life cycle management
1976:"Ending the Mortality Table"
1620:Age-adjusted life expectancy
266:Prevalence-based life tables
94:for people at different ages
7:
1613:
1507:Another common variable is
641:{\displaystyle \,\ell _{0}}
579:{\displaystyle \,\ell _{x}}
10:
2240:
2114:Human Life Table Database
1932:Roser, Max (2013-05-23).
1886:10.1080/08898489809525445
2119:Human Mortality Database
2070:. Blackwell Publishers.
1640:
1569:Ending a mortality table
1531:{\displaystyle \,m_{x}}
842:{\displaystyle \,d_{x}}
493:{\displaystyle \,(x+1)}
436:{\displaystyle \,p_{x}}
406:{\displaystyle \,(x+1)}
349:{\displaystyle \,q_{x}}
260:Multi-state life tables
2219:Statistical data types
1821:"Actuarial Life Table"
1532:
1460:
1301:
1280:
1259:
1235:
1187:
1111:
1084:
1063:
1039:
997:
867:
843:
810:
748:
642:
620:or starting point, of
604:
580:
547:
494:
461:
437:
407:
374:
350:
322:
285:Insurance applications
24:
1533:
1461:
1302:
1281:
1260:
1236:
1188:
1112:
1110:{\displaystyle \,x+t}
1085:
1064:
1040:
998:
868:
844:
811:
749:
643:
605:
581:
548:
495:
462:
438:
408:
375:
351:
309:
22:
1765:10.1136/jech.55.1.38
1656:"Cohort Life Tables"
1514:
1317:
1290:
1269:
1248:
1202:
1127:
1094:
1073:
1052:
1012:
883:
856:
825:
759:
660:
624:
593:
562:
510:
471:
467:will survive to age
450:
419:
384:
363:
332:
2052:"Life Expectancies"
1300:{\displaystyle \,k}
1279:{\displaystyle \,t}
1258:{\displaystyle \,x}
1083:{\displaystyle \,t}
1062:{\displaystyle \,x}
866:{\displaystyle \,x}
616:this is based on a
603:{\displaystyle \,x}
460:{\displaystyle \,x}
373:{\displaystyle \,x}
189:Static life tables
2093:Weisstein, Eric W.
1528:
1483:force of mortality
1456:
1297:
1276:
1255:
1231:
1183:
1107:
1080:
1059:
1035:
993:
863:
839:
806:
744:
638:
600:
576:
543:
490:
457:
433:
403:
370:
346:
323:
289:In order to price
249:Healthy Life Years
25:
2224:Survival analysis
2209:Actuarial science
2096:"Life expectancy"
2034:Sociology and You
1938:Our World in Data
1934:"Life Expectancy"
1721:Bell, Felicitie.
1635:Survival analysis
1454:
1265:will survive for
1181:
1069:will survive for
791:
29:actuarial science
2231:
2103:
2081:
2062:
2060:
2059:
2047:
2019:
2018:
2016:
2015:
1992:
1983:
1982:
1980:
1972:
1966:
1965:
1954:
1948:
1947:
1945:
1944:
1929:
1923:
1922:
1920:
1919:
1912:Health Knowledge
1904:
1898:
1897:
1869:
1863:
1862:
1860:
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1849:
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1817:
1808:
1801:
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1208:
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1190:
1189:
1184:
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1179:
1170:
1169:
1154:
1149:
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1139:
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1133:
1116:
1114:
1113:
1108:
1089:
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1086:
1081:
1068:
1066:
1065:
1060:
1044:
1042:
1041:
1036:
1034:
1033:
1024:
1023:
1018:
1002:
1000:
999:
994:
992:
991:
979:
978:
963:
962:
941:
940:
928:
927:
909:
908:
896:
895:
872:
870:
869:
864:
848:
846:
845:
840:
838:
837:
815:
813:
812:
807:
805:
804:
792:
790:
789:
780:
779:
764:
753:
751:
750:
745:
743:
742:
730:
729:
714:
713:
692:
691:
679:
678:
647:
645:
644:
639:
637:
636:
609:
607:
606:
601:
585:
583:
582:
577:
575:
574:
552:
550:
549:
544:
542:
541:
523:
522:
499:
497:
496:
491:
466:
464:
463:
458:
442:
440:
439:
434:
432:
431:
412:
410:
409:
404:
379:
377:
376:
371:
355:
353:
352:
347:
345:
344:
148:
136:
2239:
2238:
2234:
2233:
2232:
2230:
2229:
2228:
2199:
2198:
2110:
2088:
2086:Further reading
2078:
2057:
2055:
2050:
2044:
2028:
2023:
2022:
2013:
2011:
2001:Washington Post
1993:
1986:
1978:
1974:
1973:
1969:
1956:
1955:
1951:
1942:
1940:
1930:
1926:
1917:
1915:
1906:
1905:
1901:
1870:
1866:
1856:
1854:
1847:
1841:
1832:
1819:
1818:
1811:
1802:
1798:
1745:
1741:
1731:
1729:
1727:Social Security
1719:
1704:
1695:
1693:
1684:
1683:
1674:
1664:
1662:
1654:Harper, Begon.
1652:
1648:
1643:
1625:Decrement table
1616:
1599:
1571:
1522:
1518:
1515:
1512:
1511:
1502:
1479:
1448:
1444:
1425:
1421:
1406:
1402:
1401:
1399:
1384:
1380:
1374:
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1371:
1362:
1358:
1352:
1350:
1349:
1340:
1336:
1324:
1322:
1321:
1318:
1315:
1314:
1291:
1288:
1287:
1270:
1267:
1266:
1249:
1246:
1245:
1225:
1221:
1209:
1207:
1206:
1203:
1200:
1199:
1175:
1171:
1159:
1155:
1153:
1144:
1140:
1134:
1132:
1131:
1128:
1125:
1124:
1095:
1092:
1091:
1074:
1071:
1070:
1053:
1050:
1049:
1029:
1025:
1019:
1017:
1016:
1013:
1010:
1009:
987:
983:
974:
970:
958:
954:
936:
932:
917:
913:
904:
900:
891:
887:
884:
881:
880:
857:
854:
853:
833:
829:
826:
823:
822:
800:
796:
785:
781:
769:
765:
763:
760:
757:
756:
738:
734:
725:
721:
709:
705:
687:
683:
668:
664:
661:
658:
657:
632:
628:
625:
622:
621:
594:
591:
590:
570:
566:
563:
560:
559:
537:
533:
518:
514:
511:
508:
507:
472:
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468:
451:
448:
447:
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417:
416:
385:
382:
381:
364:
361:
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340:
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333:
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302:The mathematics
287:
234:mortality rates
160:
159:
158:
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156:
149:
141:
140:
137:
126:
108:Social Security
92:life expectancy
45:actuarial table
41:mortality table
39:(also called a
17:
12:
11:
5:
2237:
2227:
2226:
2221:
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2191:
2189:Ehemu Database
2186:
2181:
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2171:
2166:
2161:
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2144:
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2121:
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2109:
2108:External links
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343:
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316:
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274:marital status
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187:
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177:
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143:
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2043:0-07-828576-3
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1998:
1991:
1989:
1977:
1971:
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1913:
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1508:
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1470:
1449:
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786:
782:
776:
773:
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766:
755:
739:
735:
731:
726:
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718:
710:
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688:
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680:
675:
672:
669:
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633:
629:
619:
615:
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613:
612:
597:
588:
571:
567:
558:
557:
538:
534:
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506:
505:
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261:
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246:
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235:
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217:
216:public health
211:
209:
205:
201:
196:
192:
184:
182:
178:
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173:
169:
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164:
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101:
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81:
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38:
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2000:
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1952:
1941:. Retrieved
1937:
1927:
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1914:. 2010-06-28
1911:
1902:
1880:(1): 29–49.
1877:
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1851:
1804:
1803:Saskia Hin,
1799:
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1756:
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1730:. Retrieved
1726:
1694:. Retrieved
1692:. 2016-07-21
1689:
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1659:
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1603:epidemiology
1600:
1597:Epidemiology
1576:
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270:labor force
224:comorbidity
200:immigration
195:equilibrium
183:life tables
174:life tables
85:probability
61:John Graunt
2214:Population
2203:Categories
2058:2008-01-16
2026:References
2014:2018-03-29
1981:. soa.org.
1943:2018-04-12
1918:2018-03-30
1732:9 February
1696:2018-03-30
1665:9 February
272:states or
253:disability
204:emigration
124:Background
37:life table
33:demography
2100:MathWorld
2009:0190-8286
1852:Upcommons
1773:0143-005X
1446:ℓ
1423:ℓ
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666:ℓ
630:ℓ
568:ℓ
531:−
291:insurance
153:remaining
57:longevity
2155:(LAMBdA)
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1825:Archived
1791:11112949
1614:See also
2149:(LAHMD)
2143:(USMDB)
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276:states.
238:smoking
100:biology
2131:(AHMD)
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208:period
191:sample
181:Cohort
172:static
168:Period
69:cohort
2137:(JMD)
1979:(PDF)
1848:(PDF)
1641:Notes
1582:ages.
1307:years
1117:years
618:radix
222:term
49:death
2072:ISBN
2038:ISBN
2005:ISSN
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1859:2015
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1769:ISSN
1734:2015
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1660:Tiem
247:and
102:and
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35:, a
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