# Stretched Exponential Survival Analysis for South Korean Females
## 3 Results and Discussion
### Characteristic Life Analysis  
The comparison in the increase rate of \(\alpha\) for South Korea with that for major industrialized countries is shown in Figure 2. The increase rate in \(\alpha\) was obtained from Figure 1b for South Korea, 1987-2016 (data from the Korean Statistical Information Service, [[http://kosis.kr/eng](http://kosis.kr/eng)]([http://kosis.kr/eng](http://kosis.kr/eng))), and from literature [14] for other countries, 1980-2010 (data from the Human Mortality Database, [[http://www.mortality.org](http://www.mortality.org)]([http://www.mortality.org](http://www.mortality.org))). The error bars were taken from the standard errors by linear fits. The increase rate in \(\alpha\) per decade was evaluated as \(\sim\)2.88 years for South Korea, \(\sim\)2.71 years for Japan, \(\sim\)1.96 years for France, \(\sim\)1.85 years for Australia, \(\sim\)1.61 years for Switzerland, \(\sim\)1.49 years for UK, \(\sim\)1.24 years for Sweden, and \(\sim\)0.76 years for USA. This analysis result confirms the highest increase rate of the characteristic life for women in South Korea among the representative high-income countries including Japan, France, Australia, Switzerland, UK, Sweden, and USA.  
To demonstrate the association of the characteristic life (\(\alpha\)), taken from Figure 2, with the life expectancy at birth (\(\varepsilon\)), the annual increase rates of \(\alpha\) and \(\varepsilon\) are compared in Figure 3. The \(\varepsilon\) values for 1980-2015 were taken from the Organization for Economic Cooperation and Development [16] and  
Figure 2: Comparison in the increase rate of the characteristic life per decade among representative industrialized countries. The data were taken for South Korea (1987–2016) from the Korean Statistical Information Service ([[http://kosis.kr/eng](http://kosis.kr/eng)]([http://kosis.kr/eng](http://kosis.kr/eng))) and for other countries (1980–2010) from the Human Mortality Database ([[http://www.mortality.org](http://www.mortality.org)]([http://www.mortality.org](http://www.mortality.org))).  
the increase rates of the \(\varepsilon\) values were achieved by linear fits (the error bars taken from the standard errors: some of the error bars are smaller than the symbol sizes). The increase rates of the \(\varepsilon\) values per decade were evaluated as \(\sim\)4.15 years for South Korea, \(\sim\)2.33 years for Japan, \(\sim\)2.15 years for France, \(\sim\)1.96 years for Australia, \(\sim\)1.78 years for Switzerland, \(\sim\)1.93 years for UK, \(\sim\)1.43 years for Sweden, and \(\sim\)1.06 years for USA. The annual increase rate of the \(\varepsilon\) values (marked by \(m\)) is proportionally correlated with the annual increase rate of the \(\alpha\) values (marked by \(n\)) as \(n\approx 1.173\)\(m-0.046\) (adj. \(R^{2}\sim 0.85243\)) except for South Korea. This analysis result suggests that the annual increase rate of the \(\varepsilon\) values for South Korea looks an extraordinary case among the representative high-income countries.  
The highest increase rate in the female lifespan (in both \(\alpha\) and \(\varepsilon\)) for South Korea in Figure 3 is consistent with that the female life expectancy at birth in South Korea is the sixth ranked in 2010 and expected to be the first ranked in 2030 among the 35 industrialized countries [4]. So far, little attention has been given to South Korea in research on human health and longevity except for a few reports [4]. This analysis supports that South Korea has the highest increase rate in the female lifespan in the world in the past three decades.