little about wealth distribution, and thus the level of poverty
As mentioned before, those are NOT the same thing. Income distribution in North Korea is probably very good, people are equally poor. But they still starve to death when the crops fail.
Wealth distribution does NOT measure poverty.
Besides, HDI includes wealth distribution.
But yes, it sais very little about pensioners incomes.
No one said they are the same thing. One needs both the average and the distribution to calculate the level of poverty (be it absolute or relative), and you ignored one of these.
Nope. The sole figure in HDI related to wealth (but not equivalent with wealth, ask the Irish) is per capita GDP, which is an average. Check the formula. *Lunatic*, n. One whose delusions are out of fashion.
