lpetrich
Contributor
Here is the special case of N equally-sized entities: f = 1/N
Information: I = log(N)
Effective number (square measure, GG measure): N
For a power-law decline, \( f_k = (1 - u) \cdot u^k \) for parameter u and k starting at 0.
Information: \( \displaystyle{ I = - \log(1-u) - \frac{u}{1-u} \log(u) } \)
Effective number (square measure): \( \displaystyle{ <N> \ = \frac{1+u}{1-u} } \)
For this distribution, the GG measure too difficult to calculate.
Information: I = log(N)
Effective number (square measure, GG measure): N
For a power-law decline, \( f_k = (1 - u) \cdot u^k \) for parameter u and k starting at 0.
Information: \( \displaystyle{ I = - \log(1-u) - \frac{u}{1-u} \log(u) } \)
Effective number (square measure): \( \displaystyle{ <N> \ = \frac{1+u}{1-u} } \)
For this distribution, the GG measure too difficult to calculate.