sen_chandrasekaran_III_instantaneous2: Log-space instantaneous sensitivity via Chandrasekaran III decomposition

Description

Estimates the sensitivity of life expectancy to small changes in mortality rates using the Chandrasekaran III decomposition and log-transformed perturbations. The method perturbs mx up and down in log space and averages the directional sensitivities to approximate the derivative.

Specifically: $$m_x^{1} = \exp(\ln m_x + h)$$ $$m_x^{2} = \exp(\ln m_x - h)$$ and applies sen_chandrasekaran_III(mx1, mx2, ...) and sen_chandrasekaran_III(mx2, mx1, ...), returning their average.

Usage

sen_chandrasekaran_III_instantaneous2(
  mx,
  age = (1:length(mx1)) - 1,
  nx = rep(1, length(mx1)),
  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 version uses symmetric log-space perturbations. It gives numerically identical results to sen_arriaga_sym_instantaneous2(), sen_lopez_ruzicka_instantaneous2(), and sen_chandrasekaran_II_instantaneous2().

Examples

Run this code

a <- 0.001
b <- 0.07
x <- 0:100
mx <- a * exp(x * b)
s <- sen_chandrasekaran_III_instantaneous2(mx, age = x)
# \donttest{
plot(x, s, type = "l")
# }