In actuarial science, a life table (sometimes called a mortality table) is basically a table which shows, for a person at each age, what the probability is that they die before their next birthday. From this starting point, a number of statistics can be derived and thus also included in the table: Actuarial science applies mathematical and statistical methods to finance and insurance, particularly to the assessment of risk. ... Statistics is a broad mathematical discipline which studies ways to collect, summarize and draw conclusions from data. ...

• the probability of surviving any particular year of age
• remaining life expectancy for people at different ages
• the proportion of the original birth cohort still alive.

Life tables are usually constructed separately for men and for women because of their substantially different mortality rates. Other characteristics can also be used to distinguish different risks, such as smoking-status, occupation, socio-economic class, and others. Life expectancy is the most likely number of years remaining for a living being (or the average for a class of living beings) of a given age to live. ... Mortality rate (the word mortality comes from mortal, which originates from Latin mors, death) is the annual number of deaths (from a disease or at general) per 1000 people. ...

Insurance Applications

In order to price insurance products, and ensure the solvency of insurance companies through adequate reserves, actuaries must develop projections of future insured events (such as death, sickness, disability, etc.). To do this, actuaries develop mathematical models of the causes of these events, as well as the amount and timing of the events. They do this by studying the incidence and severity of these events in the recent past, developing expectations about how the drivers of these past events will change over time (for example, whether the increase in life expectancy that has been experienced by most generations over prior generations will continue) and, accordingly, develop an expectation for what the timing and amount of such events will be into the future. These expectations usually take the form of tables of percentages indicating the number of such events that will occur in a population, usually based on the age or other relevant characteristics of the population. More specifically, they may be referred to as mortality tables (if they provide rates of mortality, or death), morbidity tables (if they provide rates of disability and recovery), or by other names if they cover other decrements. Insurance, in law and economics, is a form of risk management primarily used to hedge against the risk of potential financial loss. ... Life expectancy is the most likely number of years remaining for a living being (or the average for a class of living beings) of a given age to live. ...

The Mathematics of Life Tables

To give an indication of how life tables are used, here are a few sample calculations. These samples may not be obvious to someone who has never studied probability theory, but are intended to introduce new ideas to people who have some understanding of discrete probability theory. Probability theory is the mathematical study of probability. ...

• qx: the probability that someone aged exactly x will die before their (x+1)th birthday
• px: the probability of surviving from age x to age (x+1)
  • px = 1-qx
• lx: the number of lives who are aged exactly x
  • note that this is based on a starting point of l0 lives, typically 100,000
  • l(x+1) = lx * (1-qx)
  • l(x+1)/lx = pq
• dx: the number of people who die aged x
  • dx = lx - l(x+1)

See also

• Age-adjusted life expectancy

Age-Adjusted Life Expectancy is the estimation of how long a person is expected to live based on their current age. ...

External links

• UK Government Actuary Department's Interim Life Tables
• US CDC Mortality Reports