Is there an index that would express any kind of similarity between the values in the same variable sets of two observations, for example the distribution of energy-sources of two countries.
I work with a panel data of the energy mix of countries where each observation of a country has a set of variables for energy-sources expressed as shares of all energy consumed by origin. The variables are the same across panels and could for example be {coal, oil, nuclear, wind, hydro, other} with no missing data and {0.2, 0.2, 0.4, 0.1, 0.0, 0.1} as an example observation.
I wish to compare the similarity of the energy-mix of each country-pair expressed as a single measure, for example between 0 and 1.
Given whatever definition of similarity you find appropriate, how should I reason to compute a pair-wise similarity index in which two countries with a similar energy mix will score highly.