Mortality models for mx approximation

Usage

mort.approx(mx, age, model = c("Brass", "Gompertz"), standard.mx = NULL, ...)

Arguments

mx: Numeric vector of age specific mortality rates.
age: Numeric vector of ages.
model: Character. Model name to be estimated. Now "Gompertz" and "Brass" are supported.
standard.mx: Numeric vector of age specific mortality rates for standard population. Default is NULL.
...: Used only for Brass model. Other parameters for the function LT() including ax (by default, the middle of the interval), sex (by default = "m" - males), l0 (by default = 1).

Value

list with estimated model and dataframe with predicted mortality rates.

Details

This function runs least squares optimization of the selected mortality function using Gauss-Newton algorithm algorithm with 2000 maximum iterations and 1e-07 as tolerance parameter. For "Gompertz" usual OLS estimator is used.

Gompertz model

The model is as follows: $$m(age) = \alpha e^{\beta age}$$

Brass model

The model is as follows: $$y(age) = \alpha + \beta y^{S}(age)$$ where $$y(age) = \frac{1}{2} ln[\frac{q(age)}{1-q(age)}]$$ and subscript S defines that function is for standard population. To get mx from qx usual formula is used: $$m(age) = \frac{q(age)}{n-q(age)(n-a(age))}$$ where n is the size of age interval and a(x) is a parameter from life table.

References

Preston, S. H., Heuveline, P., & Guillot, M. (2001). Demography: Measuring and modeling population processes. Blackwell Publishers. (pdf)

Examples


# mort.approx(mx = mx, age = 0:100, model = "Brass", standard.mx = standard.mx, sex = "m")