Beard Model - 1971

The Beard logistic hazard, \(\mu_x = A \exp(Bx) / (1 + K A \exp(Bx))\), which levels off at old age.

Usage

beard(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

beard(x = 50:100)
#> $hx
#>  [1] 0.5708676 0.6023800 0.6330658 0.6627094 0.6911267 0.7181679 0.7437196
#>  [8] 0.7677040 0.7900774 0.8108269 0.8299668 0.8475343 0.8635852 0.8781891
#> [15] 0.8914261 0.9033830 0.9141499 0.9238181 0.9324780 0.9402171 0.9471196
#> [22] 0.9532647 0.9587268 0.9635749 0.9678726 0.9716782 0.9750446 0.9780199
#> [29] 0.9806475 0.9829665 0.9850118 0.9868149 0.9884035 0.9898028 0.9910347
#> [36] 0.9921190 0.9930731 0.9939124 0.9946505 0.9952996 0.9958702 0.9963718
#> [43] 0.9968127 0.9972002 0.9975406 0.9978398 0.9981026 0.9983336 0.9985364
#> [50] 0.9987146 0.9988711
#> 
#> $par
#>     A     B     K 
#> 0.002 0.130 1.000 
#>