GOMPERTZ, BENJAMIN

(1779–1865)

Benjamin Gompertz lived his entire life in London. He came from a prominent Jewish family: His father and grandfather were diamond merchants in London; his youngest brother, Lewis, founded the Society for the Prevention of Cruelty to Animals. In 1810, he married Abigail Montefiore, whose brother, Sir Moses Montefiore, helped found the Alliance Assurance Company in 1824. Gompertz served the company as actuary and chief officer from 1824 until his retirement in 1847. In 1819, he was elected a Fellow of the Royal Society of London. He published four major papers in the Philosophical Transactions of the Society, in 1806, 1820, 1825, and 1862. He also wrote 18 other pieces, including nine on astronomical instruments.

On June 10, 1825, Gompertz's most enduring and influential research contribution was read before the Royal Society. The 72-page work, "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," was largely devoted to calculations and detailed tables. He considered and emphatically rejected the notion of a maximum lifespan. The centerpiece of his work, however, is the formula later known as Gompertz's Law, which Gompertz presented as follows: "the number of persons living at the age of x = d·g^{q^x}," where d, g, and q are parameters with, as Gompertz emphasizes, raised to the power q^x. Many demographers in the twenty-first century are more familiar with this formula in a different guise, namely that the force of mortality is an exponential function of age: µ(x) = ae^bx, where Gompertz's q equals e^b, a is the force of mortality at the initial age of 10, 30, or 50 and x is the number of years since the initial age.

Gompertz argued that "death may be the consequence of two generally co-existing causes; the one, chance … ; the other, a deterioration, or an increased inability to withstand destruction." He seems to have associated chance with the parameter a and deterioration with the parameter b. He stressed that his formula "is deserving of attention because it appears corroborated during a long portion of life by … various published tables of mortality." Although in articles published in 1860 and 1862 he applied his formula to ages as young as 10 and as old as 100, he recognized that his law was an approximation and that different values of a and b were required for different age ranges. In 1860, the British actuary William M. Makeham suggested a simple modification of Gompertz's law, μ(x) = ae^bx + c, that provided a much better fit to nineteenth-century European mortality. In developed countries of the twenty-first century, Gompertz's law captures the general pattern of the rise of mortality from about age 30 to about age 95.

BIBLIOGRAPHY

SELECTED WORKS BY BENJAMIN GOMPERTZ.

Gompertz, Benjamin. 1825. "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." Philosophical Transactions of the Royal Society 115: 513–585.

SELECTED WORKS ABOUT BENJAMIN GOMPERTZ.

Heligman, Larry, and J. H. Pollard. 1980. "The Age Pattern of Mortality." Journal of the Institute of Actuaries 107: 49–75.

Makeham, William M. 1860 "On the Law of Mortality, and the Construction of Annuity Tables." The Assurance Magazine and Journal of the Institute of Actuaries 8: 301–310.

Thatcher, A. R., V. Kannisto, and James W. Vaupel. 1998. The Force of Mortality at Ages 80 to 120. Denmark: Odense University Press.