Life table

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2003 US mortality table, Table 1, Page 1

In actuarial science and demography, a life table (also called a mortality table or actuarial table) is a table which shows, for each age, what the probability is that a person of that age will die before his or her next birthday ("probability of death"). From this starting point, a number of inferences can be derived.

Life tables are also used extensively in biology and epidemiology. The concept is also of importance in product life cycle management.

Background[edit]

There are two types of life tables:

Static life tables sample individuals assuming a stationary population with overlapping generations. "Static Life tables" and "cohort life tables" will be identical if population is in equilibrium and environment does not change. "Life table" primarily refers to period life tables, as cohort life tables can only be constructed using data up to the current point, and distant projections for future mortality.

Life tables can be constructed using projections of future mortality rates, but more often they are a snapshot of age-specific mortality rates in the recent past, and do not necessarily purport to be projections. For these reasons, the older ages represented in a life table may have a greater chance of not being representative of what lives at these ages may experience in future, as it is predicated on current advances in medicine, public health, and safety standards that did not exist in the early years of this cohort.

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, and socioeconomic class.

Life tables can be extended to include other information in addition to mortality, for instance health information to calculate health expectancy. Health expectancies such as disability-adjusted life year and Healthy Life Years are the remaining number of years a person can expect to live in a specific health state, such as free of disability. Two types of life tables are used to divide the life expectancy into life spent in various states:

Insurance applications[edit]

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, and disability). To do this, actuaries develop mathematical models of the rates and timing of the events. They do this by studying the incidence of these events in the recent past, and sometimes developing expectations of how these past events will change over time (for example, whether the progressive reductions in mortality rates in the past will continue) and deriving expected rates of such events in the future, usually based on the age or other relevant characteristics of the population. These are called mortality tables if they show death rates, and morbidity tables if they show various types of sickness or disability rates.

The availability of computers and the proliferation of data gathering about individuals has made possible calculations that are more voluminous and intensive than those used in the past (i.e. they crunch more numbers) and it is more common to attempt to provide different tables for different uses, and to factor in a range of non-traditional behaviors (e.g. gambling, debt load) into specialized calculations utilized by some institutions for evaluating risk. This is particularly the case in non-life insurance (e.g. the pricing of motor insurance can allow for a large number of risk factors, which requires a correspondingly complex table of expected claim rates). However the expression "life table" normally refers to human survival rates and is not relevant to non-life insurance.

The mathematics[edit]

tpx chart from Table 1. Life table for the total population: United States, 2003, Page 8

The basic algebra used in life tables is as follows.

\,p_x = 1-q_x
note that this is based on a radix.,[1] or starting point, of \,l_0 lives, typically taken as 100,000
\,l_{x + 1} = l_x \cdot (1-q_x) = l_x \cdot p_x
\,{l_{x + 1} \over l_x} = p_x
\,d_x = l_x-l_{x+1} = l_x \cdot (1-p_x) = l_x \cdot q_x
\,{}_tp_x = {l_{x+t} \over l_x}
\,{}_{t|k}q_x = {}_t p_x \cdot {}_k q_{x+t} = {l_{x+t} - l_{x+t+k} \over l_x}

Another common variable is

This symbol refers to Central rate of mortality. It is approximately equal to the average force of mortality, averaged over the year of age.

Ending a Mortality Table[edit]

In practice, it is useful to have an ultimate age associated with a mortality table. Once the ultimate age is reached, the mortality rate is assumed to be 1.000. This age may be the point at which life insurance benefits are paid to a survivor or annuity payments cease.

Four methods can be used to end mortality tables:[2]

Epidemiology[edit]

In epidemiology and public health, both standard life tables to calculate life expectancy and Sullivan and multistate life tables to calculate health expectancy are commonly used. The latter include information on health in addition to mortality.

See also[edit]

Notes[edit]

References[edit]

External links[edit]