scipy.stats.

exp#

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

Natural exponential of a random variable

Parameters:

XContinuousDistribution: The random variable \(X\).

Returns:

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

Examples

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

>>> import numpy as np
>>> from scipy import stats
>>> X = stats.Normal()

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

>>> Y = stats.exp(X)

To demonstrate that X represents the logarithm of Y, we plot a normalized histogram of the logarithm 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.log(y), bins=50, density=True)
>>> X.plot(ax=ax)
>>> plt.legend(('PDF of `X`', 'histogram of `log(y)`'))
>>> plt.show()