`scipy.stats._distribution_infrastructure:log`

source: /scipy/stats/_distribution_infrastructure.py :5769

Signature

def log ( X , / )

Summary

Natural logarithm of a non-negative random variable

Parameters

X : `ContinuousDistribution`: The random variable $X$ with positive support.

Returns

Y : `ContinuousDistribution`: A random variable $Y = lo g (X)$ .

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 dev-arrayapi for more information.

Examples

Suppose we have a gamma distributed random variable :math:`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 :math:`Y`, a random variable whose natural exponential is :math:`X`. If :math:`X` is to be the natural exponential of :math:`Y`, then we must take :math:`Y` to be the natural logarithm of :math:`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(435383595582522)
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()

✓