In case of creating an index using standardised variables(between 0 and 1), how do we deal with the zeroes(while using Geometric mean for aggregation)? it could be the case that only one indicator is zero while other indicators are high? Anyone has any idea how do they deal with for instance in the case of calculating the HDI?
Best Answer
Assuming "HDI" is the UN Human Development Index (first Google hit), defined by Wikipedia as something like
$$mathrm{HDI}=sqrt[3]{mathrm{Longevity}timesmathrm{Education}timesmathrm{Income}}$$
then $mathrm{HDI}=0$ if any of the three contributing indices is $0$. This makes sense, in terms of what HDI is trying to measure (e.g. a certain minimum standard is required in all three categories to count as "developed").
In Matlab, this result would happen automatically for your case, as log(0)=-Inf and your indices are all non-negative and finite, giving log_HDI=-Inf and exp(log_HDI)=0. I cannot say what would happen on other platforms. (I think Matlab follows the IEEE standard here. I have seen some platforms that define their own non-IDE types, so you should check.)
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