expand_lx() transforms a five-year abridged life table into a
one-year complete life table using the Elandt–Johnson method.
A numeric vector representing the number of survivors (\(l_x\))
at the beginning of each age interval in the abridged life table. The
vector should correspond to age intervals provided in sage.
Numeric vector of starting ages for the age groups,
default is c(0, 1, seq(5, 85, 5)).
Numeric value specifying the max age of the output estimated lx(fitlx) and mx (fitmx).
A list containing:
A numeric vector representing the estimated number of survivors at each single year of age from 0 to 100.
A numeric vector representing the estimated central death rates (\(m_x\)) for each single year of age from 0 to 100.
Baili, P., Micheli, A., Montanari, A., & Capocaccia, R. (2005). Comparison of Four Methods for Estimating Complete Life Tables from Abridged Life Tables Using Mortality Data Supplied to EUROCARE-3. Mathematical Population Studies, 12(4), 183–198. https://doi.org/10.1080/08898480500301751
# Example abridged life table data (normalized to a radix of 1)
lx <- c(
100000, 99498.39, 99294.62, 99173.88, 99047.59, 98840.46,
98521.16, 98161.25, 97636.99, 96900.13, 95718.96, 93930.91,
91463.21, 87131.41, 80525.02, 70907.59, 58090.75, 41630.48,
24019.33
)
lx <- lx / 100000
expand_lx(lx)
#> $fitlx
#> [1] 1.000000000 0.994983900 0.994304537 0.993754859 0.993309597 0.992946200
#> [7] 0.992644701 0.992387537 0.992158374 0.991946916 0.991738800 0.991559060
#> [13] 0.991347165 0.991096388 0.990805228 0.990475900 0.990146402 0.989778116
#> [19] 0.989366890 0.988909653 0.988404600 0.987828760 0.987212916 0.986565920
#> [25] 0.985896357 0.985211600 0.984552899 0.983875355 0.983167860 0.982417917
#> [31] 0.981612500 0.980705363 0.979728767 0.978681787 0.977563049 0.976369900
#> [37] 0.975129994 0.973793402 0.972340482 0.970750272 0.969001300 0.967057696
#> [43] 0.964918540 0.962569391 0.959997044 0.957189600 0.954059096 0.950697339
#> [49] 0.947116296 0.943321677 0.939309100 0.935255836 0.930870900 0.926047151
#> [55] 0.920671732 0.914632100 0.907632896 0.899826798 0.891186182 0.881688768
#> [61] 0.871314100 0.860165097 0.848051422 0.834905389 0.820659692 0.805250200
#> [67] 0.788512450 0.770535568 0.751308576 0.730824120 0.709075900 0.686309280
#> [73] 0.662182445 0.636612889 0.609534445 0.580907500 0.550378334 0.518493866
#> [79] 0.485392675 0.451254958 0.416304800 0.380810946 0.345085560 0.309480475
#> [85] 0.274380479 0.240193300 0.207336178 0.176219242 0.147226296 0.120694131
#> [91] 0.096891961 0.076003005 0.058110507 0.043190385 0.031112291 0.021649946
#> [97] 0.014500329 0.009309887 0.005704549 0.003319473 0.001824413
#>
#> $fitmx
#> [1] 0.0050287229 0.0006830210 0.0005529797 0.0004481607 0.0003659114
#> [6] 0.0003036867 0.0002591035 0.0002309476 0.0002131515 0.0002098278
#> [11] 0.0001812540 0.0002137218 0.0002529973 0.0002938187 0.0003324396
#> [16] 0.0003327221 0.0003720199 0.0004155588 0.0004622586 0.0005108472
#> [21] 0.0005827656 0.0006236256 0.0006555918 0.0006789103 0.0006947944
#> [26] 0.0006688121 0.0006884115 0.0007193483 0.0007630738 0.0008201671
#> [31] 0.0009245562 0.0009963060 0.0010692143 0.0011437613 0.0012212793
#> [36] 0.0012707215 0.0013716207 0.0014931349 0.0016367844 0.0018032956
#> [41] 0.0020077953 0.0022144750 0.0024375255 0.0026759527 0.0029287141
#> [46] 0.0032758761 0.0035298582 0.0037738668 0.0040145440 0.0042627408
#> [51] 0.0043244915 0.0046995143 0.0051954468 0.0058216052 0.0065816393
#> [56] 0.0076819105 0.0086376992 0.0096489341 0.0107142412 0.0118365910
#> [61] 0.0128781878 0.0141830712 0.0156228608 0.0172098923 0.0189554831
#> [66] 0.0210048414 0.0230623792 0.0252693615 0.0276436252 0.0302102564
#> [71] 0.0326342016 0.0357872566 0.0393793535 0.0434663010 0.0481039243
#> [76] 0.0539856150 0.0596777239 0.0659699946 0.0729257066 0.0806148116
#> [81] 0.0891146367 0.0985106621 0.1088973812 0.1203792500 0.1330717385
#> [86] 0.1471024914 0.1626126119 0.1797580810 0.1987113256 0.2196629532
#> [91] 0.2428236683 0.2684263914 0.2967286020 0.3280149273 0.3626000048
#> [96] 0.4008316468 0.4430943379 0.4898131021 0.5414577764 0.5985477367
#> [101] 0.5985477367
#>