Version of Awkward Array

2.8.10

Description and code to reproduce

Calling ak.moment with a weight array produces inflated results starting at n=2. The documentation states the formula. For weighted data this should evaluate to Σ weight * x**n / Σ weight, matching the usual definition of raw moments and aligning with the implementation of ak.var. However, the current implementation computes (x * weight) ** n before the reduction, effectively raising each weight to the nth power. This produces incorrect results whenever weights differ from 1.

import awkward as ak

data = ak.Array([1.0, 2.0])
weight = ak.Array([2.0, 3.0])

# Expected second raw moment: (2*1.0**2 + 3*2.0**2) / (2 + 3) = 14 / 5 = 2.8
expected = (2 * 1.0**2 + 3 * 2.0**2) / (2 + 3)

observed = ak.moment(data, 2, weight=weight, axis=None)

print("expected", expected)
print("observed", observed)

expected 2.8
observed 8.0

Note: This issue was identified by an automated testing tool for academic research and manually verified. If you have any concerns about this type of reporting, please let me know, and I will adjust my workflow accordingly.