De Moivre Mortality Law - 1725

The oldest law in the catalogue: survivorship falls linearly to zero at a limiting age, \(l_x = N - x\), so the hazard rises steeply as age approaches \(N\), \(\mu_x = 1/(N - x)\). A historical baseline rather than a curve to graduate data with. USE WITH CARE: the hazard is defined only below \(N\), so a prediction past the fitted ages can be negative, and MortalityLaw warns whenever it fits this law.

Usage

demoivre(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

demoivre(x = 0:95)
#> $hx
#>  [1] 0.009090909 0.009174312 0.009259259 0.009345794 0.009433962 0.009523810
#>  [7] 0.009615385 0.009708738 0.009803922 0.009900990 0.010000000 0.010101010
#> [13] 0.010204082 0.010309278 0.010416667 0.010526316 0.010638298 0.010752688
#> [19] 0.010869565 0.010989011 0.011111111 0.011235955 0.011363636 0.011494253
#> [25] 0.011627907 0.011764706 0.011904762 0.012048193 0.012195122 0.012345679
#> [31] 0.012500000 0.012658228 0.012820513 0.012987013 0.013157895 0.013333333
#> [37] 0.013513514 0.013698630 0.013888889 0.014084507 0.014285714 0.014492754
#> [43] 0.014705882 0.014925373 0.015151515 0.015384615 0.015625000 0.015873016
#> [49] 0.016129032 0.016393443 0.016666667 0.016949153 0.017241379 0.017543860
#> [55] 0.017857143 0.018181818 0.018518519 0.018867925 0.019230769 0.019607843
#> [61] 0.020000000 0.020408163 0.020833333 0.021276596 0.021739130 0.022222222
#> [67] 0.022727273 0.023255814 0.023809524 0.024390244 0.025000000 0.025641026
#> [73] 0.026315789 0.027027027 0.027777778 0.028571429 0.029411765 0.030303030
#> [79] 0.031250000 0.032258065 0.033333333 0.034482759 0.035714286 0.037037037
#> [85] 0.038461538 0.040000000 0.041666667 0.043478261 0.045454545 0.047619048
#> [91] 0.050000000 0.052631579 0.055555556 0.058823529 0.062500000 0.066666667
#> 
#> $par
#>   N 
#> 110 
#>