entropy — SciPy v1.15.3 Manual (original) (raw)

scipy.stats.Mixture.

Mixture.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 NotImplementedErrorwill be raised.

Returns:

outarray

The entropy of the random variable.

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

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