The function defined by

which is used in actuarial science for specifying a simplified mortality law (Kenney and Keeping 1962, pp. 241-242). Using  as the probability that a newborn will achieve age , the Makeham law (1860) uses

for , , , .

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.

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

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

Makeham, W. M. "On an Application of the Theory of the Composition of Decremental Forces." J. Inst. Actuaries and Assur. Mag. 18, 317-322, 1874.