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 support for Python Array API Standard compatible backends in addition to NumPy. 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 an 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()