diff --git a/xarray/namedarray/_array_api/statistical_functions.py b/xarray/namedarray/_array_api/statistical_functions.py
index 8aa1db92a7f..d99f0f812ef 100644
--- a/xarray/namedarray/_array_api/statistical_functions.py
+++ b/xarray/namedarray/_array_api/statistical_functions.py
@@ -17,6 +17,23 @@
 )
 
 
+def max(
+    x: NamedArray[Any, _DType],
+    /,
+    *,
+    dims: _Dims | Default = _default,
+    keepdims: bool = False,
+    axis: _AxisLike | None = None,
+) -> NamedArray[Any, _DType]:
+    xp = _get_data_namespace(x)
+    axis_ = _dims_to_axis(x, dims, axis)
+    d = xp.max(x._data, axis=axis_, keepdims=False)  # We fix keepdims later
+    # TODO: Why do we need to do the keepdims ourselves?
+    dims_, data_ = _get_remaining_dims(x, d, axis_, keepdims=keepdims)
+    out = x._new(dims=dims_, data=data_)
+    return out
+
+
 def mean(
     x: NamedArray[Any, _DType],
     /,
@@ -82,3 +99,54 @@ def mean(
     dims_, data_ = _get_remaining_dims(x, d, axis_, keepdims=keepdims)
     out = x._new(dims=dims_, data=data_)
     return out
+
+
+def min(
+    x: NamedArray[Any, _DType],
+    /,
+    *,
+    dims: _Dims | Default = _default,
+    keepdims: bool = False,
+    axis: _AxisLike | None = None,
+) -> NamedArray[Any, _DType]:
+    xp = _get_data_namespace(x)
+    axis_ = _dims_to_axis(x, dims, axis)
+    d = xp.min(x._data, axis=axis_, keepdims=False)  # We fix keepdims later
+    # TODO: Why do we need to do the keepdims ourselves?
+    dims_, data_ = _get_remaining_dims(x, d, axis_, keepdims=keepdims)
+    out = x._new(dims=dims_, data=data_)
+    return out
+
+
+def prod(
+    x: NamedArray[Any, _DType],
+    /,
+    *,
+    dims: _Dims | Default = _default,
+    keepdims: bool = False,
+    axis: _AxisLike | None = None,
+) -> NamedArray[Any, _DType]:
+    xp = _get_data_namespace(x)
+    axis_ = _dims_to_axis(x, dims, axis)
+    d = xp.prod(x._data, axis=axis_, keepdims=False)  # We fix keepdims later
+    # TODO: Why do we need to do the keepdims ourselves?
+    dims_, data_ = _get_remaining_dims(x, d, axis_, keepdims=keepdims)
+    out = x._new(dims=dims_, data=data_)
+    return out
+
+
+def sum(
+    x: NamedArray[Any, _DType],
+    /,
+    *,
+    dims: _Dims | Default = _default,
+    keepdims: bool = False,
+    axis: _AxisLike | None = None,
+) -> NamedArray[Any, _DType]:
+    xp = _get_data_namespace(x)
+    axis_ = _dims_to_axis(x, dims, axis)
+    d = xp.sum(x._data, axis=axis_, keepdims=False)  # We fix keepdims later
+    # TODO: Why do we need to do the keepdims ourselves?
+    dims_, data_ = _get_remaining_dims(x, d, axis_, keepdims=keepdims)
+    out = x._new(dims=dims_, data=data_)
+    return out