scipy.stats.

log#

scipy.stats.log(X, /)[source]#

Natural logarithm of a non-negative random variable

Parameters:

XContinuousDistribution: The random variable \(X\) with positive support.

Returns:

YContinuousDistribution: A random variable \(Y = \log(X)\).

Notes

Array API Standard Support

log has experimental support for Python Array API Standard compatible backends in addition to NumPy. Please consider testing these features by setting an environment variable SCIPY_ARRAY_API=1 and providing CuPy, PyTorch, JAX, or Dask arrays as array arguments. The following combinations of backend and device (or other capability) are supported.

Library	CPU	GPU
NumPy	✅	n/a
CuPy	n/a	⛔
PyTorch	⛔	⛔
JAX	⛔	⛔
Dask	⛔	n/a

See Support for the array API standard for more information.

Examples

Suppose we have a gamma distributed random variable \(X\):

>>> import numpy as np
>>> from scipy import stats
>>> Gamma = stats.make_distribution(stats.gamma)
>>> X = Gamma(a=1.0)

We wish to have a exp-gamma distributed random variable \(Y\), a random variable whose natural exponential is \(X\). If \(X\) is to be the natural exponential of \(Y\), then we must take \(Y\) to be the natural logarithm of \(X\).

>>> Y = stats.log(X)

To demonstrate that X represents the exponential of Y, we plot a normalized histogram of the exponential of observations of Y against the PDF underlying X.

>>> import matplotlib.pyplot as plt
>>> rng = np.random.default_rng()
>>> y = Y.sample(shape=10000, rng=rng)
>>> ax = plt.gca()
>>> ax.hist(np.exp(y), bins=50, density=True)
>>> X.plot(ax=ax)
>>> plt.legend(('PDF of `X`', 'histogram of `exp(y)`'))
>>> plt.show()