e sample size. If ``None`` (the default), it
    uses the heuristic value

    .. math::
        \left \lfloor \sqrt{n} + 0.5 \right \rfloor

    where :math:`n` is the sample size. This heuristic was originally
    proposed in [2]_ and has become common in the literature.
base : float, optional
    The logarithmic base to use, defaults to ``e`` (natural logarithm).
axis : int, optional
    The axis along which the differential entropy is calculated.
    Default is 0.
method : {'vasicek', 'van es', 'ebrahimi', 'correa', 'auto'}, optional
    The method used to estimate the differential entropy from the sample.
    Default is ``'auto'``.  See Notes for more information.

Returns
-------
entropy : float
    The calculated differential entropy.

Notes
-----
This function will converge to the true differential entropy in the limit

.. math::
    n \to \infty, \quad m \to \infty, \quad \frac{m}{n} \to 0

The optimal choice of ``window_length`` for a given sample size depends on
the (unknown) distribution. Typically, the smoother the density of the
distribution, the larger the optimal value of ``window_length`` [1]_.

The following options are available for the `method` parameter.

* ``'vasicek'`` uses the estimator presented in [1]_. This is
  one of the first and most influential estimators of differential entropy.
* ``'van es'`` uses the bias-corrected estimator presented in [3]_, which
  is not only consistent but, under some conditions, asymptotically normal.
* ``'ebrahimi'`` uses an estimator presented in [4]_, which was shown
  in simulation to have smaller bias and mean squared error than
  the Vasicek estimator.
* ``'correa'`` uses the estimator presented in [5]_ based on local linear
  regression. In a simulation study, it had consistently smaller mean
  square error than the Vasiceck estimator, but it is more expensive to
  compute.
* ``'auto'`` selects the method automatically (default). Currently,
  this selects ``'van es'`` for very small samples (<10), ``'ebrahimi'``
  for moderate sample sizes (11-1000), and ``'vasicek'`` for larger
  samples, but this behavior is subject to change in future versions.

All estimators are implemented as described in [6]_.

References
----------
.. [1] Vasicek, O. (1976). A test for normality based on sample entropy.
       Journal of the Royal Statistical Society:
       Series B (Methodological), 38(1), 54-59.
.. [2] Crzcgorzewski, P., & Wirczorkowski, R. (1999). Entropy-based
       goodness-of-fit test for exponentiality. Communications in
       Statistics-Theory and Methods, 28(5), 1183-1202.
.. [3] Van Es, B. (1992). Estimating functionals related to a density by a
       class of statistics based on spacings. Scandinavian Journal of
       Statistics, 61-72.
.. [4] Ebrahimi, N., Pflughoeft, K., & Soofi, E. S. (1994). Two measures
       of sample entropy. Statistics & Probability Letters, 20(3), 225-234.
.. [5] Correa, J. C. (1995). A new estimator of entropy. Communications
       in Statistics-Theory and Methods, 24(10), 2439-2449.
.. [6] Noughabi, H. A. (2015). Entropy Estimation Using Numerical Methods.
       Annals of Data Science, 2(2), 231-241.
       https://link.springer.com/article/10.1007/s40745-015-0045-9

Examples
--------
>>> import numpy as np
>>> from scipy.stats import differential_entropy, norm

Entropy of a standard normal distribution:

>>> rng = np.random.default_rng()
>>> values = rng.standard_normal(100)
>>> differential_entropy(values)
1.3407817436640392

Compare with the true entropy:

>>> float(norm.entropy())
1.4189385332046727

For several sample sizes between 5 and 1000, compare the accuracy of
the ``'vasicek'``, ``'van es'``, and ``'ebrahimi'`` methods. Specifically,
compare the root mean squared error (over 1000 trials) between the estimate
and the true differential entropy of the distribution.

>>> from scipy import stats
>>> import matplotlib.pyplot as plt
>>>
>>>
>>> def rmse(res, expected):
...     '''Root mean squared error'''
...     return np.sqrt(np.mean((res - expected)**2))
>>>
>>>
>>> a, b = np.log10(5), np.log10(1000)
>>> ns = np.round(np.logspace(a, b, 10)).astype(int)
>>> reps = 1000  # number of repetitions for each sample size
>>> expected = stats.expon.entropy()
>>>
>>> method_errors = {'vasicek': [], 'van es': [], 'ebrahimi': []}
>>> for method in method_errors:
...     for n in ns:
...        rvs = stats.expon.rvs(size=(reps, n), random_state=rng)
...        res = stats.differential_entropy(rvs, method=method, axis=-1)
...        error = rmse(res, expected)
...        method_errors[method].append(error)
>>>
>>> for method, errors in method_errors.items():
...     plt.loglog(ns, errors, label=method)
>>>
>>> plt.legend()
>>> plt.xlabel('sample size')
>>> plt.ylabel('RMSE (1000 trials)')
>>> plt.title('Entropy Estimator Error (Exponential Distribution)')

Úintegralr'