Calculate ax for life table

Source: R/lifetable.R

calc_ax() calculates the average number of person-years lived in the interval by those dying in the interval (ax) based on age-specific mortality rates (mx), starting ages (sage), and sex.

calc_ax(mx, sage, sex = "male")

Arguments

mx

Numeric vector of age-specific mortality rates.

sage

Numeric vector of starting ages for the age groups.

sex

Character string specifying the sex: "male", "female", or "total" (default is "male").

Value

A numeric vector of ax values.

Details

For most age groups, \(a_x = n_x / 2\), where \(n_x\) is the width of the age interval. For the infant group (age 0), ax is adjusted based on sex and m0:

  • Male: if m0 >= 0.1, ax=0.33; else 0.045 + 2.684 * m0

  • Female: if m0 >= 0.1, ax=0.35; else 0.053 + 2.8 * m0

  • Total: if m0 >= 0.1, ax=0.34; else 0.049 + 2.742 * m0

References

  • Coale, A. J., Demeny, P., & Vaughan, B. (1983). Regional Model Life Tables and Stable Populations (2nd ed.). New York: Academic Press.

  • Preston, S. H., Heuveline, P., & Guillot, M. (2001). Demography: Measuring and Modeling Population Processes. Malden, MA: Blackwell Publishers.

Examples

mx <- c(0.05, 0.01, 0.005) 
sage <- c(0, 1, 5)
calc_ax(mx, sage, "male")
#> [1] 0.1792 2.0000    Inf