LEdecomp (version 1.0.4)

sen_arriaga_sym: Estimate sensitivity of life expectancy using a symmetrical Arriaga approach.

Description

This approach conducts a classic Arriaga decomposition in both directions, averaging the (sign-adjusted) result, i.e. a_avg = (arriaga(mx1,mx2, ...) - arriaga(mx2, mx1, ...)) / 2, then approximates the sensitivity by dividing out the rate differences, i.e. s = a_avg / (mx2 - mx1). A resulting decomposition will be exact because the two arriaga directions are exact, but this method might be vulnerable to 0s in the denominator.

Usage

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

Value

numeric vector of life expectancy sensitivity to perturbations in mx evaluated at the average of mx1 and mx2.

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.

See Also

arriaga

Examples

a <- .001
b <- .07
x <- 0:100
mx1 <- a * exp(x * b)
mx2 <- a/2 * exp(x * b)
s <- sen_arriaga_sym(mx1, mx2, age = x)

e01 <- mx_to_e0(mx1,age=x)
e02 <- mx_to_e0(mx2,age=x)
(Delta <- e02 - e01)
deltas <- mx2- mx1
sum(deltas * s)
mx_avg <- (mx1+mx2) / 2
# \donttest{
mx_avg <- (mx1 + mx2) / 2
plot(x, s, type = 'l')
lines(x, sen_arriaga_instantaneous(mx_avg, age=x),col = "blue")
# }