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

Notes

Array API Standard Support

exp 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 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()