Makeham Mortality Law - 1860

The Gompertz hazard plus a constant, \(\mu_x = A \exp(Bx) + C\), so that the age-independent component of mortality is represented too.

Usage

makeham(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

makeham(x = 45:90)
#> $hx
#>  [1]  0.07044688  0.08008807  0.09106774  0.10357170  0.11781157  0.13402833
#>  [7]  0.15249643  0.17352844  0.19748028  0.22475732  0.25582119  0.29119761
#> [13]  0.33148527  0.37736601  0.42961629  0.48912040  0.55688536  0.63405803
#> [19]  0.72194445  0.82203200  0.93601455  1.06582111  1.21364850  1.38199853
#> [25]  1.57372032  1.79205854  2.04070830  2.32387771  2.64635907  3.01360999
#> [31]  3.43184576  3.90814453  4.45056709  5.06829330  5.77177743  6.57292513
#> [37]  7.48529488  8.52432743  9.70760720 11.05515979 12.58979092 14.33747241
#> [43] 16.32778170 18.59440241 21.17569441 24.11534300
#> 
#> $par
#>      A      B      C 
#> 0.0002 0.1300 0.0010 
#> 
#> $Sx
#>  [1] 5.612054e-01 5.205698e-01 4.779303e-01 4.336686e-01 3.882864e-01
#>  [6] 3.424066e-01 2.967638e-01 2.521822e-01 2.095384e-01 1.697087e-01
#> [11] 1.335039e-01 1.015960e-01 7.444789e-02 5.225683e-02 3.492648e-02
#> [16] 2.207667e-02 1.309529e-02 7.225501e-03 3.671379e-03 1.698360e-03
#> [21] 7.060100e-04 2.598534e-04 8.326128e-05 2.278229e-05 5.208023e-06
#> [26] 9.701308e-07 1.431282e-07 1.619195e-08 1.353763e-09 8.020907e-11
#> [31] 3.210537e-12 8.221657e-14 1.266017e-15 1.092322e-17 4.872683e-20
#> [36] 1.025459e-22 9.172885e-26 3.097047e-29 3.447458e-33 1.084575e-37
#> [41] 8.091744e-43 1.172415e-48 2.627651e-55 7.030283e-63 1.671657e-71
#> [46] 2.524353e-81
#>