Fixing gh-17749 requires a small API change to `stats.moment`

Hey all,

I suggested a rather simple fix for [gh-17749][1], and it's a sort of non-breaking API change. I was replied in a comment that such a change should go through this mailing list. Here's the Gist of the fix, without unit tests and without docs updates. I will appreciate comments/reviews:

[1]: https://github.com/scipy/scipy/issues/17749

```patch
commit f16d2282bd34726960d511c1ed277ba2754d285e
Author: Doron Behar <[email protected]>
Date:   Sat Feb 4 14:50:02 2023 +0200

    stats: Allow computing non central moments

diff --git a/result b/result
new file mode 120000
index 000000000..5cff41b90
--- /dev/null
+++ b/result
@@ -0,0 +1 @@
+/nix/store/38g1b2ai2k35kq7jw0ffm5la90zaqa0h-python3.10-scipy-1.11.0-dirty-flake
\ No newline at end of file
diff --git a/scipy/stats/_mstats_basic.py b/scipy/stats/_mstats_basic.py
index 2d10561d2..7676c7798 100644
--- a/scipy/stats/_mstats_basic.py
+++ b/scipy/stats/_mstats_basic.py
@@ -2551,7 +2551,7 @@ def winsorize(a, limits=None, inclusive=(True, True), inplace=False,
                                    upinc, contains_nan, nan_policy)
 
 
-def moment(a, moment=1, axis=0):
+def moment(a, moment=1, mean=None, axis=0):
     """
     Calculates the nth moment about the mean for a sample.
 
@@ -2561,13 +2561,15 @@ def moment(a, moment=1, axis=0):
        data
     moment : int, optional
        order of central moment that is returned
+    mean : float, optional
+       If True, then the moments are computed centralized. Default is True.
     axis : int or None, optional
        Axis along which the central moment is computed. Default is 0.
        If None, compute over the whole array `a`.
 
     Returns
     -------
-    n-th central moment : ndarray or float
+    n-th (central) moment : ndarray or float
        The appropriate moment along the given axis or over all values if axis
        is None. The denominator for the moment calculation is the number of
        observations, no degrees of freedom correction is done.
@@ -2592,8 +2594,11 @@ def moment(a, moment=1, axis=0):
 
     # for array_like moment input, return a value for each.
     if not np.isscalar(moment):
-        mean = a.mean(axis, keepdims=True)
-        mmnt = [_moment(a, i, axis, mean=mean) for i in moment]
+        if mean is None:
+            _mean = a.mean(axis, keepdims=True)
+        else:
+            _mean = mean
+        mmnt = [_moment(a, i, axis, mean=_mean) for i in moment]
         return ma.array(mmnt)
     else:
         return _moment(a, moment, axis)
diff --git a/scipy/stats/_stats_py.py b/scipy/stats/_stats_py.py
index 32445bedf..70d098baa 100644
--- a/scipy/stats/_stats_py.py
+++ b/scipy/stats/_stats_py.py
@@ -1046,14 +1046,14 @@ def moment(a, moment=1, axis=0, nan_policy='propagate'):
 
     Notes
     -----
-    The k-th central moment of a data sample is:
+    The k-th moment of a data sample is:
 
     .. math::
 
-        m_k = \frac{1}{n} \sum_{i = 1}^n (x_i - \bar{x})^k
+        m_k = \frac{1}{n} \sum_{i = 1}^n (x_i)^k
 
-    Where n is the number of samples and x-bar is the mean. This function uses
-    exponentiation by squares [1]_ for efficiency.
+    Where n is the number of samples. This function uses exponentiation by
+    squares [1]_ for efficiency.
 
     Note that, if `a` is an empty array (``a.size == 0``), array `moment` with
     one element (`moment.size == 1`) is treated the same as scalar `moment`
```
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