Makeham Curve

The function defined by

$$y=ks^xb^{q^x}$$

which is used in actuarial science for specifying a simplified mortality law. Using $s(x)$ as the probability that a newborn will achieve age $x$, the Makeham law (1860) uses

$$s(x) = \mathop{\rm exp}\nolimits (-A x - B(c^x - 1))$$

for $B > 0$, $A \geq -B$, $c > 1$, $x \geq 0$.

See also Gompertz Curve, Life Expectancy, Logistic Growth Curve, Population Growth

References

Bowers, N. L. Jr.; Gerber, H. U.; Hickman, J. C.; Jones, D. A.; and Nesbitt, C. J. Actuarial Mathematics. Itasca, IL: Society of Actuaries, p. 71, 1997.

Makeham, W. M. ``On the Law of Mortality, and the Construction of Annuity Tables.'' J. Inst. Actuaries and Assur. Mag. 8, 301-310, 1860.