Is there a Limit to Compression? References

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.

 

Is there a Limit to Compression? References

Measuring the Compression of Mortality
Väinö Kannisto
© 2000 Max-Planck-Gesellschaft ISSN 1435-9871
http://www.demographic-research.org/Volumes/Vol3/6