`scipy.stats._probability_distribution:_ProbabilityDistribution.logentropy`

source: /scipy/stats/_probability_distribution.py :1818

Signature

def logentropy ( self , * , method )

Summary

Logarithm of the differential entropy

Extended Summary

In terms of probability density function $f (x)$ and support $χ$ , the differential entropy (or simply "entropy") of a continuous random variable $X$ is:

h (X) = - \int_{χ} f (x) lo g f (x) d x

The definition for a discrete random variable is analogous, with the PMF replacing the PDF and a sum over the support replacing the integral.

logentropy computes the logarithm of the differential entropy ("log-entropy"), $lo g (h (X))$ , but it may be numerically favorable compared to the naive implementation (computing $h (X)$ then taking the logarithm).

Parameters

method : {None, 'formula', 'logexp', 'quadrature}

The strategy used to evaluate the log-entropy. By default (None), the infrastructure chooses between the following options, listed in order of precedence.

'formula': use a formula for the log-entropy itself
'logexp': evaluate the entropy and take the logarithm
'quadrature': numerically log-integrate (or, in the discrete case, log-sum) the logarithm of the entropy integrand (summand)

Not all method options are available for all distributions. If the selected method is not available, a NotImplementedError will be raised.

Returns

out : array: The log-entropy.

Notes

The differential entropy of a continuous distribution can be negative. In this case, the log-entropy is complex with imaginary part $π$ . For consistency, the result of this function always has complex dtype, regardless of the value of the imaginary part.

Examples

Instantiate a distribution with the desired parameters:

import numpy as np
from scipy import stats
X = stats.Uniform(a=-1., b=1.)

✓

Evaluate the log-entropy:

X.logentropy()

✗

np.allclose(np.exp(X.logentropy()), X.entropy())

✓

For a random variable with negative entropy, the log-entropy has an imaginary part equal to `np.pi`.

X = stats.Uniform(a=-.1, b=.1)

✓

X.entropy(), X.logentropy()

✗

Aliases

scipy.stats._distribution_infrastructure._ProbabilityDistribution.logentropy