Lifetable

A life table, or actuarial life table, is a statistical table that summarizes the mortality experience of a population. For each age or age interval, it shows the number of people alive at the beginning of the interval, the number who die during the interval, and the probability of dying within that interval. Life tables provide a compact summary of mortality patterns and are used in demography, actuarial science, public health, and social planning.

Typical life tables tabulate variables such as age x, l_x (number alive at the start of the age interval), d_x (deaths during the interval), q_x (probability of dying in the interval), p_x (probability of surviving the interval), L_x (person-years lived in the interval), T_x (total future person-years for those aged x), and e_x (life expectancy at age x).

Two main forms exist: cohort (generation) life tables, which follow a real birth cohort across ages; and period life tables, which apply mortality rates observed in a specific time period to all ages. Life tables can be complete (one-year age intervals) or abridged (grouped into five- or ten-year age bands).

Primary uses include calculating life expectancy, annuities and pension liabilities, insurance premiums, and planning for public health and social services. They also help researchers analyze mortality patterns by sex, geography, or socioeconomic status. Limitations include reliance on historical or cross-sectional data, potential biases in data collection, and the assumption that future mortality patterns will resemble past experience.

Historically, early life tables emerged in the 17th and 18th centuries, with Edmund Halley producing one of the first widely known life tables in 1693 for England and Wales, which laid groundwork for actuarial and demographic methods.