

Period
Abridged Life Tables
An excel spreadsheet template for calculating life expectancy is available. Life
tables conceptually trace a cohort of newborn babies through their entire life
under the Age
Interval (x to x+n) Age
Specific Mortality Rate (_{n}M_{x}) Probability
of Dying (_{n}q_{x}) In
general for age groups; _{n}q_{x}
= 2 x n(_{n}M_{x}) The
assumption that deaths are spread evenly across the time period of life under
consideration is particularly unrealistic in the case of infants, where the
majority of deaths occur within the first few days of life.
To calculate the probability of dying for infants therefore, the infant
mortality rate is used, as the number of livebirths is an exact estimate of the
population at risk of dying. Therefore
for infant deaths we have;
_{1}q_{0} =
_{1}D_{0}/B where
B = number of livebirths over period of consideration. Another
exception occurs in the final openended age group (85+ in the lifetable
templates). As everybody within
this age group must die, the probability of dying is equal to 1,
i.e. _{¥}q_{n
}= 1.000. Persons
Alive (l_{x}) The
number of persons alive at the beginning of an age interval (l_{x+n}) is
equal to the number alive at the beginning of the previous age interval (l_{x}),
minus the numbers of persons dying within that previous age interval
over the time period considered (_{n}d_{x});
i.e. l_{x+n}
= l_{x}  _{n}d_{x} Persons
Dying (_{n}d_{x}) The
number of persons dying within a particular age interval (_{n}d_{x})
is equal to the number persons alive at the beginning of that age interval (l_{x})
multiplied by the probability of dying within that age interval (_{n}q_{x}),
i.e. _{n}d_{x}
= l_{x} x _{n}q_{x} PersonYears
Lived in Age Interval (_{n}L_{x}) A
difficulty arises with the estimation of _{1}L_{0},that is the
average number of infants alive who have not yet reached their first birthday.
Again the problem is that it cannot be assumed that infant deaths occur
uniformly throughout the 0 to 1 age interval.
For this reason ‘separation factors’ are used to weight the average
of l_{0} and l_{1} as follows; _{1}L_{0} = 0.3l_{0} + 0.7l_{1 }_{ } An additional problem lies with _{¥}L_{85}, the average number of persons alive over age 85. This is approximated from _{¥}L_{85} = _{¥}d_{85}/_{¥}M_{85. }_{ }
Person
Years Lived From Age x (T_{x})
Life
Expectancy (e_{x})
i.e. e_{x} = T_{x}/l_{x} 
