Add unbiased computation to kurtosis

Author: raulcd

cpp/src/arrow/compute/kernels/aggregate_var_std.cc

@@ -212,7 +212,7 @@ struct StatisticImpl : public ScalarAggregator {
           out->value = std::make_shared<DoubleScalar>(state.moments.Skew(bias));
           break;
         case StatisticType::Kurtosis:
-          out->value = std::make_shared<DoubleScalar>(state.moments.Kurtosis());
+          out->value = std::make_shared<DoubleScalar>(state.moments.Kurtosis(bias));
           break;
         default:
           return Status::NotImplemented("Unsupported statistic type ",

cpp/src/arrow/compute/kernels/aggregate_var_std_internal.h

@@ -96,9 +96,17 @@ struct Moments {
     return result;
   }
 
-  double Kurtosis() const {
+  double Kurtosis(bool bias = true) const {
+    double result;
     // This may return NaN for m2 == 0 and m4 == 0, which is expected
-    return count * m4 / (m2 * m2) - 3;
+    if (bias) {
+      result = count * m4 / (m2 * m2) - 3;
+    } else {
+      result = 1.0 / (count - 2) / (count - 3) *
+               ((pow(count, 2) - 1.0) * (m4 / count) / pow((m2 / count), 2.0) -
+                3 * pow((count - 1), 2.0));
+    }
+    return result;
   }
 
   void MergeFrom(int level, const Moments& other) { *this = Merge(level, *this, other); }

python/pyarrow/tests/test_compute.py

@@ -3841,7 +3841,11 @@ def test_pivot_wider():
 
 
 @pytest.mark.pandas
-def test_biased_skew():
-    arrow_skew = pc.skew([1.0, 2.0, 3.0, 40.0, None], skip_nulls=True, bias=False)
-    pandas_skew = pd.Series(np.array([1.0, 2.0, 3.0, 40.0, np.nan])).skew(skipna=True)
+def test_biased_skew_and_kurtosis():
+    input = [1.0, 2.0, 3.0, 40.0, None]
+    arrow_skew = pc.skew(input, skip_nulls=True, bias=False)
+    pandas_skew = pd.Series(np.array(input)).skew(skipna=True)
     assert arrow_skew == pa.scalar(pandas_skew)
+    arrow_kurtosis = pc.kurtosis(input, skip_nulls=True, bias=False)
+    pandas_kurtosis = pd.Series(np.array(input)).kurtosis(skipna=True)
+    assert arrow_kurtosis == pa.scalar(pandas_kurtosis)