ENH: implement pd.Series.corr(method="distance")
Distance correlation (https://en.wikipedia.org/wiki/Distance_correlation) is a powerful yet underused technique for comparing two distributions that I think would make a very nice addition to the existing correlation methods in `pandas`.  For one, these measures have the unique property that two random variables $X$ and $Y$ are independent if and only if their distance correlation is zero, which cannot be said of Pearson, Spearman or Kendall.

The below code is an implementation in pure `numpy` (which could certainly be optimized / more elegantly written) that could be part of the `Series` class and then called within `corr`.  Later it could be integrated seamlessly with `corrwith`, and if this feature were available I know personally it would be one of the first things I would look at when approaching a regression problem.

```python
# self and other can be assumed to be aligned already
def nandistcorr(self, other):
    n = len(self)
    a = np.zeros(shape=(n, n))
    b = np.zeros(shape=(n, n))

    for i in range(n):
        for j in range(i+1, n):
            a[i, j] = abs(self[i] - self[j])
            b[i, j] = abs(other[i] - other[j])

    a = a + a.T
    b = b + b.T

    a_bar = np.vstack([np.nanmean(a, axis=0)] * n)
    b_bar = np.vstack([np.nanmean(b, axis=0)] * n)

    A = a - a_bar - a_bar.T + np.full(shape=(n, n), fill_value=a_bar.mean())
    B = b - b_bar - b_bar.T + np.full(shape=(n, n), fill_value=b_bar.mean())

    cov_ab = np.sqrt(np.nansum(A * B)) / n
    std_a = np.sqrt(np.sqrt(np.nansum(A**2)) / n)
    std_b = np.sqrt(np.sqrt(np.nansum(B**2)) / n)

    return cov_ab / std_a / std_b
```

Here's an example that shows how distance correlation can detect relationships that the other common correlation methods miss:

```python
import numpy as np
import pandas as pd
np.random.seed(2357)

s1 = pd.Series(np.random.randn(1000))
s2 = s1**2

s1.corr(s2, method="pearson")
s1.corr(s2, method="spearman")
s1.corr(s2, method="kendall")
nandistcorr(s1.values, s2.values)
```