life_expectancy_GM: Calculate Gompertz-Makeham Life Expectancy

In m-g-h/mortality:

Description

\loadmathjax

Calculates \mjsdeqn \mathcalM_GM(t) = \frac1b \exp\left( \fraca e^btb \right ) \left( \fraca e^bxb \right)^c/b \Gamma\left( - \fraccb, \fraca e^btb \right) with the upper incomplete gamma function \mjsdeqn\Gamma(\cdot, \cdot) = \int_x^\infty t^u-1 e^-t dt, \; x>0, \quad u \in \mathbbR which is implemented in upper_inc_gamma.

Usage

life_expectancy_GM(t, A, R, alpha)

Arguments

t	numeric scalar or vector corresponding to the age(s) \mjseqnt
A	numeric scalar corresponding to the \mjseqnA parameter
R	numeric scalar corresponding to the \mjseqnR parameter
alpha	numeric scalar corresponding to the \mjseqn\alpha parameter

Value

Returns a numeric scalar giving the Gompertz-Makeham life expectancy \mjseqne_GM(t)

Sources

Castellares et al. (2020) - On closed-form expressions to Gompertz–Makeham life expectancy. Theoretical Population Biology 134 (August 2020): 53-60. https://doi.org/10.1016/j.tpb.2020.04.005

See Also

upper_inc_gamma

Examples

# You can use a single age:
life_expectancy_GM(t = 0,
                   A = 0.00033,
                   R = 0.00014,
                   alpha = 0.11521)

# Or a vector of ages:
life_expectancy_GM(t = 0:100,
                   A = 0.00033,
                   R = 0.00014,
                   alpha = 0.11521)

m-g-h/mortality documentation built on Dec. 21, 2021, 12:46 p.m.