Mode-based Measures Shortest Age Interval of Deaths

3. Concentration in Percentile Scale

In search for a general compression indicator covering the entire age range excepting childhood, we show in Figure 2 the historical development during the secular mortality transition among Finnish females. The age-at-death distribution of a life table is divided into percentiles which are placed on the horizontal scale. On the vertical scale we give the length of the age interval in which each percentile died. Thus, when in late 19th century, the lowest values were about half a year, it meant that where the concentration of deaths was greatest, about two percent of all deaths took place within one year of age. When the most recent curves reach down to a value of 0.25 years, four percent of all deaths occur in one year of age.

(Figure 2 here)

The logic of this graph is that compression presses the curves down. Periods of faster and slower compression can be identified. At the lowest point of each curve lies the mode, corresponding to the percentiles where the compression is most advanced. We can note that though the mode has moved to a higher age as shown in Table 1, it has at the same time moved to lower percentiles indicating that more people now live beyond the mode.

The progressive concentration of deaths to adult age is compensated by deconcentration at the youngest percentiles, not shown in Figure 2. In 1881-90 the first two percentiles died within 24 hours after birth, a century later within 25 years. The first semi-decile lasted in the earlier period 3 months, in the latter, 54 years. Yet even so there has been a relative concentration of mortality at the very beginning of life. As the infant death rate fell from 150 to 4 per 1000, the share of the neonatal mortality in it rose from 32 to 74 percent. The early life mode, while losing importance, has become sharper than ever.

(Figure 3 here)

Figure 3 shows in four countries the historical course of the mortality compression in terms of age span of the four quartiles. To avoid excessive volatility, the last quartile is cut off after the 99th percentile. The figures show how the heavy concentration of deaths into childhood gradually lessened during the transition. In the very beginning, even the second quartile was slightly decompressed. However, already before the turn of the century, compression of deaths into ever shorter age intervals was taking place in all quartiles except the first. In this process, the third quartile became the narrowest, followed by the second, which in all countries here shown, overtook the fourth. The inter-quartile range thus acquired an advanced position in the ongoing compression. In Table 1 (col. 6) we see the precipitous fall of the width of the inter-quartile range.


Mode-based Measures Shortest Age Interval of Deaths

Measuring the Compression of Mortality
Väinö Kannisto
© 2000 Max-Planck-Gesellschaft ISSN 1435-9871