# rotate.leecarter: Rotated Lee-Carter In PPgp/MortCast: Estimation and Projection of Age-Specific Mortality Rates

## 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

 ```1 2 3``` ```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

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13``` ```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") ```

PPgp/MortCast documentation built on Aug. 8, 2021, 5:17 p.m.