sen_chandrasekaran_II_instantaneous: Instantaneous sensitivity via Chandrasekaran II decomposition

Description

Estimates the sensitivity of life expectancy to small changes in mortality rates using the Chandrasekaran II decomposition. This is done by perturbing the input mortality rates up and down by a small factor and calculating the directional sensitivity.

Specifically, the function constructs: $$m_{x}^{1} = m_x \cdot \left(\frac{1}{1 - h}\right)$$ $$m_{x}^{2} = m_x \cdot (1 - h)$$ and applies sen_chandrasekaran_II(mx1, mx2, ...) to the result.

Usage

sen_chandrasekaran_II_instantaneous(
  mx,
  age = (1:length(mx1)) - 1,
  nx = rep(1, length(mx)),
  sex = "t",
  perturb = 1e-06,
  closeout = TRUE
)

Value

numeric vector of sensitivity of life expectancy to perturbations in mx

Arguments

mx: Numeric vector of mortality rates (central death rates).
age: integer vector of the lower bound of each age group (currently only single ages supported)
nx: integer vector of age intervals, default 1.
sex: Character; "m" for male, "f" for female, or "t" for total.
perturb: Numeric; a small constant determining the perturbation size (default 1e-6).
closeout: logical. Default TRUE. Shall we use the HMD Method Protocol to close out the ax and qx values? See details.

Details

This approach gives a reasonable approximation of the derivative of life expectancy with respect to each age-specific mortality rate. It gives numerically identical results to sen_arriaga_sym_instantaneous(), sen_lopez_ruzicka_instantaneous(), and sen_chandrasekaran_III_instantaneous().

Examples

Run this code

a <- 0.001
b <- 0.07
x <- 0:100
mx <- a * exp(x * b)
s <- sen_chandrasekaran_II_instantaneous(mx, age = x)
# \donttest{
plot(x, s, type = "l")
# }