diff --git a/pandas/compat/numpy/function.py b/pandas/compat/numpy/function.py
index f6e80aba0c34f..a36e25a9df410 100644
--- a/pandas/compat/numpy/function.py
+++ b/pandas/compat/numpy/function.py
@@ -69,25 +69,27 @@ def __call__(
         max_fname_arg_count=None,
         method: str | None = None,
     ) -> None:
-        if args or kwargs:
-            fname = self.fname if fname is None else fname
-            max_fname_arg_count = (
-                self.max_fname_arg_count
-                if max_fname_arg_count is None
-                else max_fname_arg_count
+        if not args and not kwargs:
+            return None
+
+        fname = self.fname if fname is None else fname
+        max_fname_arg_count = (
+            self.max_fname_arg_count
+            if max_fname_arg_count is None
+            else max_fname_arg_count
+        )
+        method = self.method if method is None else method
+
+        if method == "args":
+            validate_args(fname, args, max_fname_arg_count, self.defaults)
+        elif method == "kwargs":
+            validate_kwargs(fname, kwargs, self.defaults)
+        elif method == "both":
+            validate_args_and_kwargs(
+                fname, args, kwargs, max_fname_arg_count, self.defaults
             )
-            method = self.method if method is None else method
-
-            if method == "args":
-                validate_args(fname, args, max_fname_arg_count, self.defaults)
-            elif method == "kwargs":
-                validate_kwargs(fname, kwargs, self.defaults)
-            elif method == "both":
-                validate_args_and_kwargs(
-                    fname, args, kwargs, max_fname_arg_count, self.defaults
-                )
-            else:
-                raise ValueError(f"invalid validation method '{method}'")
+        else:
+            raise ValueError(f"invalid validation method '{method}'")
 
 
 ARGMINMAX_DEFAULTS = {"out": None}
@@ -247,7 +249,7 @@ def validate_cum_func_with_skipna(skipna: bool, args, kwargs, name) -> bool:
 LOGICAL_FUNC_DEFAULTS = {"out": None, "keepdims": False}
 validate_logical_func = CompatValidator(LOGICAL_FUNC_DEFAULTS, method="kwargs")
 
-MINMAX_DEFAULTS = {"axis": None, "out": None, "keepdims": False}
+MINMAX_DEFAULTS = {"axis": None, "dtype": None, "out": None, "keepdims": False}
 validate_min = CompatValidator(
     MINMAX_DEFAULTS, fname="min", method="both", max_fname_arg_count=1
 )
@@ -285,10 +287,9 @@ def validate_cum_func_with_skipna(skipna: bool, args, kwargs, name) -> bool:
 SUM_DEFAULTS["keepdims"] = False
 SUM_DEFAULTS["initial"] = None
 
-PROD_DEFAULTS = STAT_FUNC_DEFAULTS.copy()
-PROD_DEFAULTS["axis"] = None
-PROD_DEFAULTS["keepdims"] = False
-PROD_DEFAULTS["initial"] = None
+PROD_DEFAULTS = SUM_DEFAULTS.copy()
+
+MEAN_DEFAULTS = SUM_DEFAULTS.copy()
 
 MEDIAN_DEFAULTS = STAT_FUNC_DEFAULTS.copy()
 MEDIAN_DEFAULTS["overwrite_input"] = False
@@ -304,7 +305,7 @@ def validate_cum_func_with_skipna(skipna: bool, args, kwargs, name) -> bool:
     PROD_DEFAULTS, fname="prod", method="both", max_fname_arg_count=1
 )
 validate_mean = CompatValidator(
-    STAT_FUNC_DEFAULTS, fname="mean", method="both", max_fname_arg_count=1
+    MEAN_DEFAULTS, fname="mean", method="both", max_fname_arg_count=1
 )
 validate_median = CompatValidator(
     MEDIAN_DEFAULTS, fname="median", method="both", max_fname_arg_count=1
@@ -395,3 +396,21 @@ def validate_minmax_axis(axis: AxisInt | None, ndim: int = 1) -> None:
         return
     if axis >= ndim or (axis < 0 and ndim + axis < 0):
         raise ValueError(f"`axis` must be fewer than the number of dimensions ({ndim})")
+
+
+_validation_funcs = {
+    "median": validate_median,
+    "mean": validate_mean,
+    "min": validate_min,
+    "max": validate_max,
+    "sum": validate_sum,
+    "prod": validate_prod,
+}
+
+
+def validate_func(fname, args, kwargs) -> None:
+    if fname not in _validation_funcs:
+        return validate_stat_func(args, kwargs, fname=fname)
+
+    validation_func = _validation_funcs[fname]
+    return validation_func(args, kwargs)
diff --git a/pandas/core/generic.py b/pandas/core/generic.py
index 3da4f96444215..f55800c7f44e1 100644
--- a/pandas/core/generic.py
+++ b/pandas/core/generic.py
@@ -11345,10 +11345,8 @@ def _stat_function(
         numeric_only: bool_t = False,
         **kwargs,
     ):
-        if name == "median":
-            nv.validate_median((), kwargs)
-        else:
-            nv.validate_stat_func((), kwargs, fname=name)
+        assert name in ["median", "mean", "min", "max", "kurt", "skew"], name
+        nv.validate_func(name, (), kwargs)
 
         validate_bool_kwarg(skipna, "skipna", none_allowed=False)
 
@@ -11445,12 +11443,8 @@ def _min_count_stat_function(
         min_count: int = 0,
         **kwargs,
     ):
-        if name == "sum":
-            nv.validate_sum((), kwargs)
-        elif name == "prod":
-            nv.validate_prod((), kwargs)
-        else:
-            nv.validate_stat_func((), kwargs, fname=name)
+        assert name in ["sum", "prod"], name
+        nv.validate_func(name, (), kwargs)
 
         validate_bool_kwarg(skipna, "skipna", none_allowed=False)