For a given set of age groups to fit against, and a given stable growth rate, $r$, what is the error implied given the current $r$ and stationary standard?

OPAG_r_min(r, Age_fit, Pop_fit, AgeInt_fit, Lx1, Age_Lx1)

Arguments

r

given stable growth rate

Age_fit

integer vector of lower bounds for age groups of Pop_fit

Pop_fit

numeric vector of at least two population counts to use for fitting

AgeInt_fit

integer vector of widths of age groups of Pop_fit

Lx1

numeric vector of stable population standard by single ages

Age_Lx1

integer vector of lower bounds for age groups of Lx1

Value

numeric. A residual that you're presumably trying to minimize.

Details

This is a utility function for OPAG(), which needs to optimize $r$ for a given population vector and stationary standard.

Examples

# Make up some population data to fit to: Pop_fit <- c(85000,37000) Age_fit <- c(70,80) AgeInt_fit <- c(10,10) nLx <- downloadnLx(NULL, "Spain","female",1971)
#> Downloading nLx data for Spain, years 1971, gender female
# graduate(nLx, Age_nLx, method = method, constrain = TRUE) Ageab <- names2age(nLx) Lx1 <- graduate(c(nLx), Ageab, method = "mono", constrain = TRUE) Age_Lx1 <- 0:100 r <- .01 OPAG_r_min(r, Pop_fit = Pop_fit, Age_fit = Age_fit, AgeInt_fit = AgeInt_fit, Lx1 = Lx1, Age_Lx1 = Age_Lx1)
#> [1] 0.03025071
(r_opt <- optimize(OPAG_r_min, Pop_fit = Pop_fit, Age_fit = Age_fit, AgeInt_fit = AgeInt_fit, Lx1 = Lx1, Age_Lx1 = Age_Lx1, interval = c(-0.05,.05))$min)
#> [1] 0.002199804