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### Comments on the use of life tables

Here, we are going to describe columns of the complete life table: (see [4] for more details but we call W the last interval ):

1. Age interval [x,x+1[. Each interval in this column is defined by the two exact ages stated except for the final age interval.
2. Proportion of those alive at age x dying in the interval [x,x+1[, . They are derived from the corresponding age-specific deaths rates of the current population, using formulae:

where with is the age-specific death rates, the number of deaths at age x registered and is the midyear (calendar year) population during the calendar year. For a', see after.

3. Number of living persons at age x, .

For , see after.

4. Number dying in interval [x,x+1[, .

, and are related by:

5. Fraction of last year of life for age x, . Each of the people who have died during the interval [x,x+1[ has lived x complete years plus a fraction of the last year. is often considered to be 0.5 on average, except for the first fourth age groups.
6. Number of years lived by the total cohort in interval [x,x+1[, . It follows that:

Remarks:

1. The previous approximation ( ) is less valid for the first years of life (from one year of age to four). However, the result remain close enough to the more realistic one to permit also this approximation for these age groups.
2. Although the same method is used, reliability may differ between countries, for example, because of differences in methods of measuring the .

Eric Hauet
Fri Apr 25 22:40:35 DFT 1997