Life table

Usage

LT(age, sex = "m", mx, ax = NULL, w = NULL, l0 = 1)

Arguments

age: Numeric array of age intervals; for full life table = 0:100; for concise life table = c(0:1, seq(5,85,5))
sex: Character. Sex. "m" for males or "f" for females. By default = "m".
mx: Numeric array with age specific mortality rates.
ax: Optional. Numeric array with ax. By default, it is the middle of the interval, while ax for age 0 is modeled as in Andreev & Kingkade (2015).
w: Optional. Numeric array with weights for each age interval for calculating weighted life expectancy (wex).
l0: Numeric. Life table radix. By default, = 1 but it can be any positive real number. In "human" demography tradition it is 100'000, in "ecological" and "evolutionary" demography tradition it is 1.

Value

A numeric matrix with one row per age group. Standard columns are age, mx, ax, qx, lx, dx, Lx, Tx, and ex. If w is supplied, additional columns w, wLx, and wex are appended, where wex is weighted life expectancy.

Details

By default, $a_x$ for age 0 (first entity in ax) is modeled as in Andreev & Kingkade (2015, p. 390, see table 3-2).

The weighted life expectancy is calculated as follows: $$e_x^w = \frac{\sum_{i = x}^{\omega}L_x w_x}{l_x}$$ where $\omega$ is the last age, $w$ is weight s.t. $w \in [0,1]$, and other variables are life table functions.

References

Andreev, E. M., & Kingkade, W. W. (2015). Average age at death in infancy and infant mortality level: Reconsidering the Coale-Demeny formulas at current levels of low mortality. Demographic Research, 33, 363-390.

Examples

# Minimal toy example
age <- 0:5
mx <- c(0.02, 0.01, 0.012, 0.015, 0.02, 0.03)
LT(age = age, sex = "m", mx = mx)
#>      age    mx     ax      qx      lx      dx       Lx       Tx    ex
#> [1,]   0 0.020  0.109 0.01965 1.00000 0.01965  0.99785 35.69312 35.69
#> [2,]   1 0.010  0.500 0.00995 0.98035 0.00975  0.97547 34.69527 35.39
#> [3,]   2 0.012  0.500 0.01193 0.97060 0.01158  0.96481 33.71979 34.74
#> [4,]   3 0.015  0.500 0.01489 0.95902 0.01428  0.95188 32.75499 34.15
#> [5,]   4 0.020  0.500 0.01980 0.94474 0.01871  0.93539 31.80311 33.66
#> [6,]   5 0.030 33.333 1.00000 0.92603 0.92603 30.86772 30.86772 33.33
# \donttest{
if (interactive()) {
  # Real RosBris data via get_rosbris(): Russian males, 2010
  rus2010 <- subset(get_rosbris("mortality_5"),
    year == 2010 & code == 1100 & sex == "m" & territory == "t"
  )
  LT(age = rus2010$age, sex = "m", mx = rus2010$mx)
}
# }