Does the measure $\sum \frac{n_i}{n} \log^d(\frac{n}{n_i})$ has a name?

Question

Does the measure $\sum_i \frac{n_i}{n} \log^d(\frac{n}{n_i})$ has a name? - It matches the information theory's entropy when $d=1$ and $\sum_i n_i = n$, but - it does not seem to match the definition of Renyi's entropy nor other variants in higher dimensions. - Me and my student wonder if it could be used to describe the complexity of a Maxima algorithm in high dimension.

Answer 1

i have had a class in thermodynamics where i saw this measure. it was in german though and googleling the name did not get very good results though. Still i found that the English name is "uncertainty measure". the German version is "Unschärfe-maß"