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 \(Y = \exp(X)\).

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()