TABLE I.

Tested Mortality Functions

Title	Formula
Gompertz	${\mu }_b(x|b)=\exp [b_0+b_{1}x]$
Weibull	${\mu }_b(x|b)={b_0{b}_1}^{(b_0)}{}_x(b_0-1)$
Logistic	${\mu }_b(x|b)=\frac{\exp (b_0+b_{1}x)}{(1+b_2\exp (b_0)/b_1(b_{1}x)-1)}$
Additional shape-defining parameters	${\mu }_0(x|\theta )={\mu }_b(x|b)+c+\exp (a_0-a_{1}x)$
Exponential	${\mu }_b(x|b)=0$

The tested mortality (μ), functions given age (x), and parameters (b). The Gompertz, Weibull, and logistic functions were all extended by additional shape-defining parameters, the Makeham c term for age independent mortality, and an initial declining Gompertz function with parameters a₁ and a₂. The exponential function is age-independent and assumes constant mortality with age.