sen_arriaga: the sensitivity implied by a classic Arriaga decomposition

Description

The sensitivity of life expectancy to a perturbation in mortality rates can be derived by dividing the Arriaga decomposition result $\Delta$ by the difference mx2-mx1. $$s_{x} = \frac{\Delta}{_{n}M^{2}_x - _{n}M^{1}_x}$$

Usage

sen_arriaga(
  mx1,
  mx2,
  age = 0:(length(mx1) - 1),
  nx = rep(1, length(mx1)),
  sex1 = "t",
  sex2 = sex1,
  closeout = TRUE
)

Value

s numeric vector with one element per age group, and which gives the sensitivity values for each age.

Arguments

mx1: numeric vector of the mortality rates (central death rates) for population 1
mx2: numeric vector of the mortality rates (central death rates) for population 2
age: integer vector of the lower bound of each age group (currently only single ages supported)
nx: integer vector of age intervals, default 1.
sex1: character either the sex for population 1: Male ("m"), Female ("f"), or Total ("t")
sex2: character either the sex for population 2: Male ("m"), Female ("f"), or Total ("t") assumed same as sex1 unless otherwise specified.
closeout: logical. Default TRUE. Shall we use the HMD Method Protocol to close out the ax and qx values? See details.

References

arriaga1984measuringLEdecomp preston2000demographyLEdecomp

Examples

Run this code

a <- .001
b <- .07
x <- 0:100
mx1 <- a * exp(x * b)
mx2 <- a/2 * exp(x * b)
cc <- arriaga(mx1, mx2, age = x)
# examples can come from above too
s <- sen_arriaga(mx1, mx2, age = x)
# \donttest{
plot(x, s)
# }
cc_check <- s * (mx2 - mx1)
# \donttest{
plot(x,cc)
lines(x,cc_check)
# }