Gompertz Curve

The function defined by

It is used in actuHelvetica science for specifying a simplified mortality law (Kenney and Keeping 1962, p. 241). Using  as the probability that a newborn will achieve age , the Gompertz law is

for ,  (Gompertz 1832).

REFERENCES:

Bowers, N. L. Jr.; Gerber, H. U.; Hickman, J. C.; Jones, D. A.; and Nesbitt, C. J. ActuHelvetica 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, 1832.

Kenney, J. F. and Keeping, E. S. Mathematics of Statistics, Pt. 1, 3rd ed. Princeton, NJ: Van Nostrand, 1962.