The Perks logistic hazard, \(\mu_x = (A + B C^x) / (1 + D C^x)\), which flattens the Gompertz rise at the oldest ages.
Examples
perks(x = 50:100)
#> $hx
#> [1] 0.01102998 0.01148955 0.01194358 0.01239016 0.01282751 0.01325398
#> [7] 0.01366811 0.01406865 0.01445452 0.01482486 0.01517901 0.01551652
#> [13] 0.01583709 0.01614064 0.01642721 0.01669699 0.01695030 0.01718756
#> [19] 0.01740927 0.01761600 0.01780837 0.01798704 0.01815270 0.01830605
#> [25] 0.01844778 0.01857861 0.01869921 0.01881025 0.01891237 0.01900621
#> [31] 0.01909235 0.01917136 0.01924377 0.01931008 0.01937078 0.01942630
#> [37] 0.01947705 0.01952343 0.01956579 0.01960446 0.01963976 0.01967196
#> [43] 0.01970132 0.01972810 0.01975250 0.01977474 0.01979500 0.01981346
#> [49] 0.01983027 0.01984558 0.01985952
#>
#> $par
#> A B C D
#> 0.0005 0.0002 1.1000 0.0100
#>