Age decomposition of mortality: single decrement process
decomp.RdAge decomposition of mortality: single decrement process
Arguments
- mx1
Numeric array with age specific mortality rates of population 1 (base population).
- mx2
Numeric array with age specific mortality rates of population 2 (compared population).
- sex
Character. Sex. "m" for males and "f" for females. By default,
sex = "m".- age
Numeric array of age intervals; for full life table =
0:100; for concise life table =c(0:1, seq(5,85,5))- method
Character. Decomposition method. "andreev" (1982), "arriaga" (1984) or "pollard" (1982) - slightly different in their results. By default,
method = "andreev".- ax1
Optional. Numeric array with ax for the 1st population. By default, it is a the middle of the interval, while ax for age 0 is modeled as in Andreev & Kingkade (2015).
- ax2
Optional. Numeric array with ax for the 2nd population. By default, it is a the middle of the interval, while ax for age 0 is modeled as in Andreev & Kingkade (2015).
Value
dataframe with parameters of decomposition (depends on method) and decomposition in years (ex12) and percents (ex12_prc).
Details
Example of decomposition using Andreev (1982) formulas: $$\Delta_x = l_x^2(e_x^2 - e_x^1) - l_{x+n}^2(e_{x+n}^2 - e_{x+n}^1), \ \ \ x \neq \omega$$ $$\Delta_{\omega} = l_{\omega}^2(e_{\omega}^2 - e_{\omega}^1)$$ where \(\Delta_x\) is an absolute contribution of age \(x\) to difference in \(e_0\) between the second and the first population. \(e_x^i, l_x^i\) are life table functions for population \(i\). \(\omega\) is the last age group. Note, \(e_0^2 - e_0^1 = \sum_{x}^{\omega}\Delta_x\)
References
Arriaga, E. E. (1984). Measuring and explaining the change in life expectancies. Demography, 21, 83-96.
Андреев Е.М. (1982). Метод компонент в анализе продолжительности жизни. Вестник статистики, 9, 42-47.
Pollard, J. H. (1982). The expectation of life and its relationship to mortality. Journal of the Institute of Actuaries, 109(2), 225–240.
See also
mdecomp() for age and cause decomposition