duckdb · Mytherin · Jan 22, 2024 · Nov 1, 2023 · Nov 1, 2023 · Nov 28, 2023
diff --git a/src/catalog/default/default_functions.cpp b/src/catalog/default/default_functions.cpp
@@ -138,6 +138,7 @@ static DefaultMacro internal_macros[] = {
 	{DEFAULT_SCHEMA, "list_first", {"l", nullptr}, "list_aggr(l, 'first')"},
 	{DEFAULT_SCHEMA, "list_any_value", {"l", nullptr}, "list_aggr(l, 'any_value')"},
 	{DEFAULT_SCHEMA, "list_kurtosis", {"l", nullptr}, "list_aggr(l, 'kurtosis')"},
+	{DEFAULT_SCHEMA, "list_kurtosis_pop", {"l", nullptr}, "list_aggr(l, 'kurtosis_pop')"},
 	{DEFAULT_SCHEMA, "list_min", {"l", nullptr}, "list_aggr(l, 'min')"},
 	{DEFAULT_SCHEMA, "list_max", {"l", nullptr}, "list_aggr(l, 'max')"},
 	{DEFAULT_SCHEMA, "list_product", {"l", nullptr}, "list_aggr(l, 'product')"},

diff --git a/src/core_functions/aggregate/distributive/functions.json b/src/core_functions/aggregate/distributive/functions.json
@@ -86,6 +86,13 @@
         "example": "",
         "type": "aggregate_function"
     },
+    {
+        "name": "kurtosis_pop",
+        "parameters": "x",
+        "description": "Returns the excess kurtosis (Fisher’s definition) of all input values, without bias correction",
+        "example": "",
+        "type": "aggregate_function"
+    },
     {
         "name": "min",
         "parameters": "arg",

diff --git a/src/core_functions/aggregate/distributive/kurtosis.cpp b/src/core_functions/aggregate/distributive/kurtosis.cpp
@@ -14,6 +14,11 @@ struct KurtosisState {
 	double sum_four;
 };
 
+struct KurtosisFlagBiasCorrection {};
+
+struct KurtosisFlagNoBiasCorrection {};
+
+template <class KURTOSIS_FLAG>
 struct KurtosisOperation {
 	template <class STATE>
 	static void Initialize(STATE &state) {
@@ -53,7 +58,11 @@ struct KurtosisOperation {
 	template <class TARGET_TYPE, class STATE>
 	static void Finalize(STATE &state, TARGET_TYPE &target, AggregateFinalizeData &finalize_data) {
 		auto n = (double)state.n;
-		if (n <= 3) {
+		if (n <= 1) {
+			finalize_data.ReturnNull();
+			return;
+		}
+		if (std::is_same<KURTOSIS_FLAG, KurtosisFlagBiasCorrection>::value && n <= 3) {
 			finalize_data.ReturnNull();
 			return;
 		}
@@ -70,11 +79,15 @@ struct KurtosisOperation {
 		            6 * state.sum_sqr * state.sum * state.sum * temp * temp - 3 * pow(state.sum, 4) * pow(temp, 3));
 
 		double m2 = temp * (state.sum_sqr - state.sum * state.sum * temp);
-		if (m2 <= 0 || ((n - 2) * (n - 3)) == 0) { // m2 shouldn't be below 0 but floating points are weird
+		if (m2 <= 0) { // m2 shouldn't be below 0 but floating points are weird
 			finalize_data.ReturnNull();
 			return;
 		}
-		target = (n - 1) * ((n + 1) * m4 / (m2 * m2) - 3 * (n - 1)) / ((n - 2) * (n - 3));
+		if (std::is_same<KURTOSIS_FLAG, KurtosisFlagNoBiasCorrection>::value) {
+			target = m4 / (m2 * m2) - 3;
+		} else {
+			target = (n - 1) * ((n + 1) * m4 / (m2 * m2) - 3 * (n - 1)) / ((n - 2) * (n - 3));
+		}
 		if (!Value::DoubleIsFinite(target)) {
 			throw OutOfRangeException("Kurtosis is out of range!");
 		}
@@ -86,8 +99,15 @@ struct KurtosisOperation {
 };
 
 AggregateFunction KurtosisFun::GetFunction() {
-	return AggregateFunction::UnaryAggregate<KurtosisState, double, double, KurtosisOperation>(LogicalType::DOUBLE,
-	                                                                                           LogicalType::DOUBLE);
+	return AggregateFunction::UnaryAggregate<KurtosisState, double, double,
+	                                         KurtosisOperation<KurtosisFlagBiasCorrection>>(LogicalType::DOUBLE,
+	                                                                                        LogicalType::DOUBLE);
+}
+
+AggregateFunction KurtosisPopFun::GetFunction() {
+	return AggregateFunction::UnaryAggregate<KurtosisState, double, double,
+	                                         KurtosisOperation<KurtosisFlagNoBiasCorrection>>(LogicalType::DOUBLE,
+	                                                                                          LogicalType::DOUBLE);
 }
 
 } // namespace duckdb
diff --git a/src/core_functions/function_list.cpp b/src/core_functions/function_list.cpp
@@ -198,6 +198,7 @@ static StaticFunctionDefinition internal_functions[] = {
 	DUCKDB_SCALAR_FUNCTION_SET(JulianDayFun),
 	DUCKDB_AGGREGATE_FUNCTION(KahanSumFun),
 	DUCKDB_AGGREGATE_FUNCTION(KurtosisFun),
+	DUCKDB_AGGREGATE_FUNCTION(KurtosisPopFun),
 	DUCKDB_SCALAR_FUNCTION_SET(LastDayFun),
 	DUCKDB_SCALAR_FUNCTION_SET_ALIAS(LcmFun),
 	DUCKDB_SCALAR_FUNCTION_SET(LeastFun),

diff --git a/src/include/duckdb/core_functions/aggregate/distributive_functions.hpp b/src/include/duckdb/core_functions/aggregate/distributive_functions.hpp
@@ -159,6 +159,15 @@ struct KurtosisFun {
 	static AggregateFunction GetFunction();
 };
 
+struct KurtosisPopFun {
+	static constexpr const char *Name = "kurtosis_pop";
+	static constexpr const char *Parameters = "x";
+	static constexpr const char *Description = "Returns the excess kurtosis (Fisher’s definition) of all input values, without bias correction";
+	static constexpr const char *Example = "";
+
+	static AggregateFunction GetFunction();
+};
+
 struct MinFun {
 	static constexpr const char *Name = "min";
 	static constexpr const char *Parameters = "arg";

diff --git a/test/sql/aggregate/aggregates/test_kurtosis.test b/test/sql/aggregate/aggregates/test_kurtosis.test
@@ -65,6 +65,16 @@ select kurtosis(k), kurtosis(v), kurtosis(v2) from aggr;
 ----
 11.000000	-1.961428	-1.445120
 
+query III
+select kurtosis_pop(k), kurtosis_pop(v), kurtosis_pop(v2) from aggr;
+----
+6.100000	-1.676857	-1.358688
+
+query I
+with onetwo as (select range::float as v from range(1,3)) select kurtosis_pop(v) from onetwo;
+----
+-2.0
+
 query I
 select  kurtosis(v2) from aggr group by v ORDER BY ALL;
 ----

diff --git a/test/sql/function/list/aggregates/kurtosis.test b/test/sql/function/list/aggregates/kurtosis.test
@@ -35,6 +35,16 @@ NULL
 NULL
 NULL
 
+query I
+select list_kurtosis_pop(k) from aggr;
+----
+6.100000
+-1.676857
+-1.358688
+NULL
+NULL
+NULL
+
 # incorrect usage
 statement error
 select list_kurtosis()