Extropy
The extropy [LSAgro11] is a dual to the Entropy. It is defined by:
\[\X{X} = -\sum_{x \in X} (1-p(x)) \log_2 (1-p(x))\]
The entropy and the extropy satisify the following relationship:
\[\H{X} + \X{X} = \sum_{x \in \mathcal{X}} \H{p(x), 1-p(x)} = \sum_{x \in \mathcal{X}} \X{p(x), 1-p(x)}\]
Unfortunately, the extropy does not yet have any intuitive interpretation.
In [1]: from dit.other import extropy
In [2]: from dit.example_dists import Xor
In [3]: extropy(Xor())
Out[3]: 1.2451124978365313
In [4]: extropy(Xor(), [0])
Out[4]: 1.0
API
- extropy(dist, rvs=None)[source]
Returns the extropy J[X] over the random variables in rvs.
If the distribution represents linear probabilities, then the extropy is calculated with units of ‘bits’ (base-2).
- Parameters:
dist (Distribution or float) – The distribution from which the extropy is calculated. If a float, then we calculate the binary extropy.
rvs (list, None) – The indexes of the random variable used to calculate the extropy. If None, then the extropy is calculated over all random variables. This should remain None for scalar distributions.
- Returns:
J – The extropy of the distribution.
- Return type: