See the help which documents that the measure concerned is the sum of squared probabilities. This should be clear if you look at the code too or experiment with toy examples.
So, for two toy examples with probabilities 1, 0, 0, 0, 0 (maximum concentration) and 0.2 0.2 0.2 0.2 0.2 (maximum diversity) the sums of squared probabilities are, respectively 1*1 + 5* 0 * 0 = 1 and 0.2 * 0.2 * 5 = 0.04 * 5 = 0.2. 0 is unattainable with this measure, although a set-up with many very rare categories produces very small values.
You are thinking in terms of its complement, subtracted from 1.
The reciprocal is even more useful, but that's a different story.
I think Herfindahl used this version originally. Hirschman used something similar but not identical.
In short, in different literatures people variously work with this measure, its complement, and its reciprocal. People are often sloppy about which version is named what.
So, for two toy examples with probabilities 1, 0, 0, 0, 0 (maximum concentration) and 0.2 0.2 0.2 0.2 0.2 (maximum diversity) the sums of squared probabilities are, respectively 1*1 + 5* 0 * 0 = 1 and 0.2 * 0.2 * 5 = 0.04 * 5 = 0.2. 0 is unattainable with this measure, although a set-up with many very rare categories produces very small values.
You are thinking in terms of its complement, subtracted from 1.
The reciprocal is even more useful, but that's a different story.
I think Herfindahl used this version originally. Hirschman used something similar but not identical.
In short, in different literatures people variously work with this measure, its complement, and its reciprocal. People are often sloppy about which version is named what.
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