Opperman Mortality Law - 1870

A three-term hazard across the whole lifespan, \(\mu_x = A/\sqrt{x + 1} - B + C\sqrt{x + 1}\), evaluated at ages shifted by one year so the term stays finite at age 0. THIS SIGN IS A CHOICE: the published form writes the middle term with a free sign (\(+b\)); the engine estimates on the log scale and so requires positivity, hence the - B (\(b = -B < 0\)) branch, which is the branch mortality data occupy. See the opperman entry of availableLaws.

Usage

opperman(x, par = NULL)

Arguments

x

vector of age at the beginning of the age classes.

par

parameters of the selected model. If NULL the default values are assigned automatically.

Value

A list of rates and model parameters.

Examples

opperman(x = 1:25)
#> $hx
#>  [1] 0.02929848 0.02442606 0.02160000 0.01972461 0.01837942 0.01736433
#>  [7] 0.01657056 0.01593333 0.01541139 0.01497708 0.01461111 0.01429956
#> [13] 0.01403211 0.01380094 0.01360000 0.01342453 0.01327073 0.01313553
#> [19] 0.01301641 0.01291129 0.01281844 0.01273641 0.01266395 0.01260000
#> [25] 0.01254366
#> 
#> $par
#>     A     B     C 
#> 4e-02 4e-04 1e-03 
#>