Gompertz Curve

The function defined by

$$y=ab^{q^x}.$$

It 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 Gompertz law (1825) is

$$s(x) = \mathop{\rm exp}\nolimits [-m(c^x - 1)],$$

for $c > 1$, $x\geq 0$.

See also Life Expectancy, Logistic Growth Curve, Makeham 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.

Gompertz, B. ``On the Nature of the Function Expressive of the Law of Human Mortality, and on a New Mode of Determining the Value of Life Contingencies.'' Phil. Trans. Roy. Soc. London 123, 513-585, 1825.