sen_lopez_ruzicka_sym_instantaneous: Instantaneous sensitivity via symmetrical Lopez-Ruzicka decomposition

Description

Estimates the instantaneous sensitivity of life expectancy to small proportional changes in mortality rates, using the symmetrical Lopez-Ruzicka decomposition. This implementation perturbs the rates up and down around a central value and applies the symmetrical decomposition to the result.

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_lopez_ruzicka_sym(mx1, mx2, ...) to the result.

Usage

sen_lopez_ruzicka_sym_instantaneous(
  mx,
  age = 0:(length(mx) - 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 gives a pointwise estimate of the derivative of life expectancy with respect to each age-specific mortality rate, evaluated symmetrically around the given mortality schedule. It gives numerically identical results to e.g. sen_arriaga_sym_instantaneous() and sen_chandrasekaran_II_instantaneous().

Examples

Run this code

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