User:Danielkscarmo/sandbox

Generalized HDI equations:

1. Life Expectancy Index (LEI) $$= \frac{\textrm{LE} - LE_{G,min}}{LE_{G,max}-LE_{G,min}}$$

2. Education Index (EI) $$= \frac{\sqrt{\textrm{MYSI} \cdot \textrm{EYSI}}-EI_{G,min}} {EI_{G,max}-EI_{G,min}}$$


 * 2.1 Mean Years of Schooling Index (MYSI) $$= \frac{\textrm{MYS} - MYS_{G,min}}{MYS_{G,max}-MYS_{G,min}}$$


 * 2.2 Expected Years of Schooling Index (EYSI) $$= \frac{\textrm{EYS} - EYS_{G,min}}{EYS_{G,max}-EYS_{G,min}}$$

3. Income Index (II) $$= \frac{\ln(\textrm{GNIpc}) - \ln(I_{G,min})}{\ln(I_{G,max}) - \ln(I_{G,min})}$$

Goalposts for the 2013 report were set to:

$$LE_{G,max} = 83.6$$ (Japan, 2012)

$$LE_{G,min}= 20$$

$$EI_{G,max}= 0.971$$ (New Zealand, 2010)

$$EI_{G,min}= 0$$

$$MYS_{G,max}= 13.3$$ (USA, 2010)

$$MYS_{G,min}= 0$$

$$EYS_{G,max}= 18$$ (capped at)

$$EYS_{G,min}= 0$$

$$I_{G,max}= 87,478$$ (Qatar, 2012)

$$I_{G,min}= 100$$