Annex

Calculation of compression indicators C10, C25 and C50. These are defined as the narrowest age intervals in which resp. 10, 25 and 50 percent of all deaths occur.

Example: France, female, 1991-95.

Table A x d(x)   80 2954 81 3207 82 3482 83 3788 84 4044 85 4218 86 4386 87 4510 88 4561 89 4540 90 4421 91 4207 92 3903 93 3505 94 3044

Table B. No. d(x) d(x) required indicator   1 4561 4561     2 4540 9101     3 4510 13611 10000 C10 4 4421 18032     5 4386 22418     6 4218 26636 25000 C25 7 4207 30843     8 4044 34887     9 3903 38790     10 3788 42578     11 3505 46083     12 3482 49565     13 3207 52772 50000 C50

Procedure:

Table A gives the part of the age-at-death distribution required for Table B. The series has to be smooth enough so that the d(x) values decline regularly on both sides of the mode.

Table B gives the d(x) values in a contiguous area on both sides of the mode, in descending order. These are summed up until the total reaches 50000.

Each indicator equals the number of years needed for the resp. total, less the fraction of the last-added year which exceeds the specified total.

Solution:

C10 = 3-3611/4510 = 2.20 years.

C25 = 6-1636/4218 = 5.61 years.

C50 = 13-2772/3207 = 12.14 years.