Coale-Demeny 4a1. This is a rule of thumb. In this and some other older texts, 4a1 is known as a 'separation factor'. These coefficients were pulled from the PAS spreadsheets LTPOPDTH.XLS and not located in the original Manual X.

lt_rule_4a1_cd(
M0,
a0rule = "ak",
IMR = NA,
Sex = "m",
region = "w",
SRB = 1.05
)

## Arguments

M0 numeric. Event exposure infant mortality rate. character. Either "ak" (default) or "cd". numeric. Optional. q0, the death probability in first year of life, in case available separately. character. "m", "f" or "b" for male, female, or both. character. "n", "e", "s" or "w" for North, East, South, or West. sex ratio at birth.

## Value

The average age at death between ages 1-4, 4a1.

## Details

If sex is given as both, "b", then we calculate the male and female results separately, then weight them together using SRB. This is bad in theory, but the leverage is trivial, and it's better than using male or female coefs for the total population. If IMR is not given, then M0 is used in its stead.

United Nations (1983). Manual X: Indirect Techniques for Demographic Estimation, number 81. United Nations Department of International Economic and Social Affairs, New York. United States Census Bureau (2017). “Population Analysis System (PAS) Software.” https://www.census.gov/data/software/pas.html, https://www.census.gov/data/software/pas.html.

## Examples

m0 <- seq(.001,.2,by =.001)
if (FALSE) {

# using Andreev-Kingkade for a0 (it makes no difference if you use cd actually...)
plot(m0, sapply(m0, lt_rule_4a1_cd, Sex = "m", region = "e"), ylab = "4a1",
type = 'l', ylim = c(1,2), lty = 2, col = "blue")
lines(m0,sapply(m0, lt_rule_4a1_cd, Sex = "m", region = "w"), col = "blue")
lines(m0,sapply(m0, lt_rule_4a1_cd, Sex = "m", region = "n"), col = "blue", lty = "8383",lwd=2)
lines(m0,sapply(m0, lt_rule_4a1_cd, Sex = "m", region = "s"), col = "blue", lty = "6464",lwd=2)
lines(m0,sapply(m0, lt_rule_4a1_cd, Sex = "f", region = "e"), lty = 2, col = "red")
lines(m0,sapply(m0, lt_rule_4a1_cd, Sex = "f", region = "w"), col = "red")
lines(m0,sapply(m0, lt_rule_4a1_cd, Sex = "f", region = "n"), col = "red", lty = "8383",lwd=2)
lines(m0,sapply(m0, lt_rule_4a1_cd, Sex = "f", region = "s"), col = "red", lty = "6464",lwd=2)

text(.05, lt_rule_4a1_cd(.05,Sex = "m", region = "e"),"males E",font=2,pos=4)
text(.05, lt_rule_4a1_cd(.05,Sex = "m", region = "w"),"males W",font=2,pos=4)
text(.05, lt_rule_4a1_cd(.05,Sex = "m", region = "s"),"males S",font=2,pos=4)
text(.05, lt_rule_4a1_cd(.05,Sex = "m", region = "n"),"males N",font=2,pos=4)

text(0, lt_rule_4a1_cd(.01,Sex = "f", region = "e"),"females E",font=2,pos=4)
text(0, lt_rule_4a1_cd(.01,Sex = "f", region = "w"),"females W",font=2,pos=4)
text(0, lt_rule_4a1_cd(.01,Sex = "f", region = "s"),"females S",font=2,pos=4)
text(0, lt_rule_4a1_cd(.01,Sex = "f", region = "n"),"females N",font=2,pos=4)

}