## Thursday, November 8, 2012

### How to calculate expectation of life?

The age-specific death rates are calculated separately for separate groups of data which are believed to have different mortality rates (e.g. males and females, and perhaps type of residence, if data is available separately for these groups) from which one can calculate the probability of surviving to each age.
The probability of surviving from age x to age x+n is denoted as npx and the probability of dying during age x (i.e. between ages x and x+1) is denoted qx. For example, if 5% of a group of people alive at their 50th birthday die before their 51st birthday, then the age-specific death probability at age 50 would be 5%.
The life expectancy at age x, denoted as ex, is calculated as below. This is the expected number of complete years lived.  Life expectancy is by definition an arithmetic mean of number of years of life remaining at a given age
By using the theory of Expectation in the Theory of Probability, it is calculated as sum of the product of   n , npx and q x+t  ; the summation is to from n = 0 to ∞.
It is important to note that this statistic is usually based on past mortality experience, and assumes that the same age-specific mortality rates will continue into the future. Thus such life expectancy figures need to be adjusted for temporal trends before calculating how long a currently living individual of a particular age is expected to live.