DOC: Improve pandas.DataFrame.plot.density docstring

This docstring is quite similar to the one of
[PR20041](pandas-dev#20041).
Unfortunately, I was not able to compute a kernel estimate of a
two-dimensional random variable. Hence, the example is more of an
analysis of some independent data series.

pandas/plotting/_core.py

@@ -2791,26 +2791,77 @@ def hist(self, by=None, bins=10, **kwds):
 
     def kde(self, bw_method=None, ind=None, **kwds):
         """
-        Kernel Density Estimate plot
+        Generate Kernel Density Estimate plot using Gaussian kernels.
+
+        In statistics, kernel density estimation (KDE) is a non-parametric way
+        to estimate the probability density function (PDF) of a random
+        variable. This function uses Gaussian kernels and includes automatic
+        bandwith determination.
 
         Parameters
         ----------
-        bw_method: str, scalar or callable, optional
-            The method used to calculate the estimator bandwidth.  This can be
+        bw_method : str, scalar or callable, optional
+            The method used to calculate the estimator bandwidth. This can be
             'scott', 'silverman', a scalar constant or a callable.
             If None (default), 'scott' is used.
             See :class:`scipy.stats.gaussian_kde` for more information.
         ind : NumPy array or integer, optional
-            Evaluation points. If None (default), 1000 equally spaced points
-            are used. If `ind` is a NumPy array, the kde is evaluated at the
-            points passed. If `ind` is an integer, `ind` number of equally
-            spaced points are used.
-        `**kwds` : optional
-            Keyword arguments to pass on to :py:meth:`pandas.DataFrame.plot`.
+            Evaluation points for the estimated PDF. If None (default),
+            1000 equally spaced points are used. If `ind` is a NumPy array, the
+            kde is evaluated at the points passed. If `ind` is an integer,
+            `ind` number of equally spaced points are used.
+        **kwds : optional
+            Additional keyword arguments are documented in
+            :meth:`pandas.Series.plot`.
 
         Returns
         -------
         axes : matplotlib.AxesSubplot or np.array of them
+
+        See also
+        --------
+        scipy.stats.gaussian_kde : Representation of a kernel-density
+            estimate using Gaussian kernels. This is the function used
+            internally to estimate the PDF.
+        :meth:`pandas.Series.plot.kde` : Generate a KDE plot for a Series
+
+        Examples
+        --------
+        Given several Series of points randomly sampled from unknown
+        distributions, estimate their distribution using KDE with automatic
+        bandwidth determination and plot the results, evaluating them at
+        1000 equally spaced points (default):
+
+        .. plot::
+            :context: close-figs
+
+            >>> df = pd.DataFrame({
+            ...     'x': [1, 2, 2.5, 3, 3.5, 4, 5],
+            ...     'y': [4, 4, 4.5, 5, 5.5, 6, 6],
+            ... })
+            >>> ax = df.plot.kde()
+
+        A scalar bandwidth can be specified. Using a small bandwidth value can
+        lead to overfitting, while using a large bandwidth value can result
+        in underfitting:
+
+        .. plot::
+            :context: close-figs
+
+            >>> ax = df.plot.kde(bw_method=0.3)
+
+        .. plot::
+            :context: close-figs
+
+            >>> ax = df.plot.kde(bw_method=3)
+
+        Finally, the `ind` parameter determines the evaluation points for the
+        plot of the estimated PDF:
+
+        .. plot::
+            :context: close-figs
+
+            >>> ax = df.plot.kde(ind=[1, 2, 3, 4, 5, 6])
         """
         return self(kind='kde', bw_method=bw_method, ind=ind, **kwds)