Relating Rényi entropy and q-log entropy
by John from John D. Cook on (#5HYZS)
I've written before about Renyi entropy Hq and most recently q-log entropy Sq, two generalizations of Shannon entropy.
There are simple equations relating Renyi entropy and q-log entropy if we measure both in nats:
I mentioned in the post on q-log entropy that there were two possible ways it could be defined. The equation above applies to what I called in that post Sq, not S q. In other words, it applies to the version that uses lnq(1/p) and not the version that uses -lnq(p). Recall that these are not equal unless q equals 1. When q does equal 1, then Renyi entropy and q-log entropy are the same as Shannon entropy.
Source: Tom Leinster, Entropy and Diversity: The Axiomatic Approach.
The post Relating Renyi entropy and q-log entropy first appeared on John D. Cook.