William Makeham & the Gompertz–Makeham Law (1860)
Event Date: 1860 Category: Actuarial Science — Mortality Refinement / Hazard Modeling
Summary
William Makeham (1826–1891) refined Gompertz’s model by adding an age‑independent component to mortality. The resulting Gompertz–Makeham Law became the dominant mortality model of the late 19th and early 20th centuries. It allowed actuaries to account for background hazards—accidents, epidemics, environmental risks—that affect all ages.
Background / Context
By mid‑century:
- Gompertz’s model worked well for adult mortality
- but it failed to capture age‑independent risks
- insurers needed a more flexible model
Makeham provided the missing piece.
What Happened
⭐ 1. Makeham’s Modification (1860)
Makeham proposed:
μ(x) = A + Be^{Cx} (mortality = age‑independent risk + age‑dependent exponential risk)
This allowed actuaries to model:
- accidents
- epidemics
- environmental hazards
- baseline mortality
⭐ Sidebar: Why Makeham’s Addition Mattered
The first model to separate background risk from aging
Makeham’s insight:
- mortality has two components
- one that increases with age
- one that does not
This made mortality modeling more realistic and more useful for insurers.
Impact
- Improved pricing accuracy
- Better fit to observed mortality
- Dominant model for decades
- Foundation for 20th‑century actuarial science
Why It Mattered (Plain English)
Makeham made Gompertz’s model practical in the real world, where people die from more than just aging.
