MortCast (version 2.7-0)

rotate.leecarter: Rotated Lee-Carter

Description

Rotate the Lee-Carter parameter \(b_x\) over time to reach an ultimate \(b^u_x\), as described in Li et al. (2013).

Usage

rotate.leecarter(bx, ultimate.bx, e0, e0l = 80, e0u = 102, p = 0.5)
ultimate.bx(bx)

Arguments

bx

A vector of the Lee-Carter \(b_x\) parameter (from e.g. lileecarter.estimate or leecarter.estimate).

ultimate.bx

A vector of the ultimate \(b^u_x\) parameter as defined in Li, Lee, Gerland (2013) (obtained using lileecarter.estimate or ultimate.bx).

e0

A time series of life expectancies.

e0l

Level of life expectancy at which the rotation starts.

e0u

Level of life expectancy at which the rotation finishes.

p

Exponent of the smooth function.

Value

Function rotate.leecarter returns a matrix of rotated \(B_x(t)\) where rows correspond to age groups and columns correspond to time periods (given by the vector e0).

Function ultimate.bx returns a vector of the ultimate \(b^u_x\).

References

Li, N., Lee, R. D. and Gerland, P. (2013). Extending the Lee-Carter method to model the rotation of age patterns of mortality decline for long-term projections. Demography, 50, 2037-2051.

Examples

# NOT RUN {
data(mxF, mxM, e0Fproj, e0Mproj, package = "wpp2017")
country <- "Japan"
mxm <- subset(mxM, name == country)[,4:16]
mxf <- subset(mxF, name == country)[,4:16]
e0f <- as.numeric(subset(e0Fproj, name == country)[-(1:2)])
e0m <- as.numeric(subset(e0Mproj, name == country)[-(1:2)])
rownames(mxm) <- rownames(mxf) <- c(0,1, seq(5, 100, by=5))
lc <- lileecarter.estimate(mxm, mxf)
rotlc <- rotate.leecarter(lc$bx, lc$ultimate.bx, (e0f + e0m)/2)
plot(lc$bx, type="l")
lines(lc$ultimate.bx, col="red")
for(i in 1:ncol(rotlc)) lines(rotlc[,i], col="grey")
  
# }