diff --git a/heat/core/statistics.py b/heat/core/statistics.py
index 3ce8dd4791..c2a9b43b66 100644
--- a/heat/core/statistics.py
+++ b/heat/core/statistics.py
@@ -1091,9 +1091,7 @@ def median(
 DNDarray.median.__doc__ = median.__doc__
 
 
-def __merge_moments(
-    m1: torch.Tensor, m2: torch.Tensor, correction: bool = True
-) -> Tuple[torch.Tensor, ...]:
+def __merge_moments(m1: Tuple, m2: Tuple, correction: bool = True) -> Tuple[torch.Tensor, ...]:
     """
     Merge two statistical moments.
     If the length of ``m1`` and ``m2`` (must be equal) is ``==3`` then the second moment (variance)
@@ -1120,6 +1118,8 @@ def __merge_moments(
     if len(m1) != len(m2):
         raise ValueError(f"m1 and m2 must be same length, currently {len(m1)} and {len(m2)}")
     n1, n2 = m1[-1], m2[-1]
+    if n2.sum() == 0:
+        return m1
     mu1, mu2 = m1[-2], m2[-2]
     n = n1 + n2
     delta = mu2 - mu1
diff --git a/tests/core/test_statistics.py b/tests/core/test_statistics.py
index 51811288bd..27bb793e48 100644
--- a/tests/core/test_statistics.py
+++ b/tests/core/test_statistics.py
@@ -1,6 +1,7 @@
 import numpy as np
 import torch
 import os
+import unittest
 
 from itertools import combinations
 from scipy import stats as ss
@@ -1599,3 +1600,12 @@ def test_var(self):
 
         # edge case from #2374
         self.assertEqual(ht.var(ht.array([0.], split=None), axis=0, ddof=0), 0)
+
+    @unittest.skipUnless(ht.communication.MPI_WORLD.size >= 3, "Test requires at least 3 tasks")
+    def test_first_two_leading_ranks_empty(self):
+        comm = self.comm
+        local_data = torch.tensor([], dtype=torch.float32) if comm.rank < 2 else torch.tensor([comm.rank], dtype=torch.float32)
+        data = ht.DNDarray(local_data, gshape=(comm.size-2,), dtype=ht.float32, split=0, device=ht.devices.cpu, comm=comm, balanced=False)
+
+        self.assertEqual(ht.mean(data), np.mean(data.numpy()))
+        self.assertEqual(ht.var(data), np.var(data.numpy()))