sen_lopez_ruzicka_instantaneous: Instantaneous sensitivity via Lopez-Ruzicka decomposition

Description

Estimates the sensitivity of life expectancy to small changes in mortality rates using the Lopez-Ruzicka decomposition. This is done by perturbing the input mortality rates up and down by a small factor and averaging the resulting directional sensitivities to approximate a symmetric derivative.

Specifically: $$m_x^{1} = m_x \cdot \left( \frac{1}{1 - h} \right)$$ $$m_x^{2} = m_x \cdot (1 - h)$$ and applies sen_lopez_ruzicka(mx1, mx2, ...) and sen_lopez_ruzicka(mx2, mx1, ...), returning their average.

Usage

sen_lopez_ruzicka_instantaneous(
  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 method gives numerically identical results to sen_arriaga_sym_instantaneous(), sen_chandrasekaran_II_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_lopez_ruzicka_instantaneous(mx, age = x)
# \donttest{
plot(x, s, type = "l")
# }