scipy.stats.Normal.

entropy#

Normal.entropy(*, method=None)[source]#

Differential entropy

In terms of probability density function \(f(x)\) and support \(\chi\), the differential entropy (or simply “entropy”) of a continuous random variable \(X\) is:

\[h(X) = - \int_{\chi} f(x) \log f(x) dx\]
Parameters:
method{None, ‘formula’, ‘logexp’, ‘quadrature’}

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

  • 'formula': use a formula for the entropy itself

  • 'logexp': evaluate the log-entropy and exponentiate

  • 'quadrature': use numerical integration

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

Returns:
outarray

The entropy of the random variable.

See also

logentropy
pdf

Notes

This function calculates the entropy using the natural logarithm; i.e. the logarithm with base \(e\). Consequently, the value is expressed in (dimensionless) “units” of nats. To convert the entropy to different units (i.e. corresponding with a different base), divide the result by the natural logarithm of the desired base.

References

[1]

Differential entropy, Wikipedia, https://en.wikipedia.org/wiki/Differential_entropy

Examples

Instantiate a distribution with the desired parameters:

>>> from scipy import stats
>>> X = stats.Uniform(a=-1., b=1.)

Evaluate the entropy:

>>> X.entropy()
0.6931471805599454
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