kurtosis udaf

README.md

@@ -86,3 +86,4 @@ SELECT min_by(x, y) FROM VALUES (1, 10), (2, 5), (3, 15), (4, 8) as tab(x, y);
 - [x] `min_by(expression1, expression2) -> scalar` - Returns the value of `expression1` associated with the minimum value of `expression2`.
 - [x] `skewness(expression) -> scalar` - Computes the skewness value for `expression`.
 - [x] `kurtois_pop(expression) -> scalar` - Computes the excess kurtosis (Fisher’s definition) without bias correction.
+- [x] `kurtosis(expression) -> scalar` - Computes the excess kurtosis (Fisher’s definition) with bias correction according to the sample size.

src/kurtosis.rs

@@ -0,0 +1,195 @@
+// Licensed to the Apache Software Foundation (ASF) under one
+// or more contributor license agreements.  See the NOTICE file
+// distributed with this work for additional information
+// regarding copyright ownership.  The ASF licenses this file
+// to you under the Apache License, Version 2.0 (the
+// "License"); you may not use this file except in compliance
+// with the License.  You may obtain a copy of the License at
+//
+//   http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing,
+// software distributed under the License is distributed on an
+// "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+// KIND, either express or implied.  See the License for the
+// specific language governing permissions and limitations
+// under the License.
+
+use arrow::array::{ArrayRef, Float64Array, UInt64Array};
+use arrow::datatypes::{DataType, Field};
+use datafusion::arrow;
+use std::any::Any;
+use std::fmt::Debug;
+
+use datafusion::common::cast::as_float64_array;
+use datafusion::common::downcast_value;
+use datafusion::common::DataFusionError;
+use datafusion::error::Result;
+use datafusion::logical_expr::function::{AccumulatorArgs, StateFieldsArgs};
+use datafusion::logical_expr::{Accumulator, AggregateUDFImpl, Signature, Volatility};
+use datafusion::scalar::ScalarValue;
+
+make_udaf_expr_and_func!(
+    KurtosisFunction,
+    kurtosis,
+    x,
+    "Calculates the excess kurtosis (Fisher’s definition) with bias correction according to the sample size.",
+    kurtosis_udaf
+);
+
+pub struct KurtosisFunction {
+    signature: Signature,
+}
+
+impl Debug for KurtosisFunction {
+    fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
+        f.debug_struct("KurtosisFunction")
+            .field("signature", &self.signature)
+            .finish()
+    }
+}
+
+impl Default for KurtosisFunction {
+    fn default() -> Self {
+        Self::new()
+    }
+}
+
+impl KurtosisFunction {
+    pub fn new() -> Self {
+        Self {
+            signature: Signature::coercible(vec![DataType::Float64], Volatility::Immutable),
+        }
+    }
+}
+
+impl AggregateUDFImpl for KurtosisFunction {
+    fn as_any(&self) -> &dyn Any {
+        self
+    }
+
+    fn name(&self) -> &str {
+        "kurtosis"
+    }
+
+    fn signature(&self) -> &Signature {
+        &self.signature
+    }
+
+    fn return_type(&self, _arg_types: &[DataType]) -> Result<DataType> {
+        Ok(DataType::Float64)
+    }
+
+    fn accumulator(&self, _acc_args: AccumulatorArgs) -> Result<Box<dyn Accumulator>> {
+        Ok(Box::new(KurtosisAccumulator::new()))
+    }
+
+    fn state_fields(&self, _args: StateFieldsArgs) -> Result<Vec<Field>> {
+        Ok(vec![
+            Field::new("count", DataType::UInt64, true),
+            Field::new("sum", DataType::Float64, true),
+            Field::new("sum_sqr", DataType::Float64, true),
+            Field::new("sum_cub", DataType::Float64, true),
+            Field::new("sum_four", DataType::Float64, true),
+        ])
+    }
+}
+
+/// Accumulator for calculating the excess kurtosis (Fisher’s definition) with bias correction according to the sample size.
+/// This implementation follows the [DuckDB implementation]:
+/// <https://github.com/duckdb/duckdb/blob/main/src/core_functions/aggregate/distributive/kurtosis.cpp>
+#[derive(Debug, Default)]
+pub struct KurtosisAccumulator {
+    count: u64,
+    sum: f64,
+    sum_sqr: f64,
+    sum_cub: f64,
+    sum_four: f64,
+}
+
+impl KurtosisAccumulator {
+    pub fn new() -> Self {
+        Self {
+            count: 0,
+            sum: 0.0,
+            sum_sqr: 0.0,
+            sum_cub: 0.0,
+            sum_four: 0.0,
+        }
+    }
+}
+
+impl Accumulator for KurtosisAccumulator {
+    fn update_batch(&mut self, values: &[ArrayRef]) -> Result<()> {
+        let array = as_float64_array(&values[0])?;
+        for value in array.iter().flatten() {
+            self.count += 1;
+            self.sum += value;
+            self.sum_sqr += value.powi(2);
+            self.sum_cub += value.powi(3);
+            self.sum_four += value.powi(4);
+        }
+        Ok(())
+    }
+
+    fn merge_batch(&mut self, states: &[ArrayRef]) -> Result<()> {
+        let counts = downcast_value!(states[0], UInt64Array);
+        let sums = downcast_value!(states[1], Float64Array);
+        let sum_sqrs = downcast_value!(states[2], Float64Array);
+        let sum_cubs = downcast_value!(states[3], Float64Array);
+        let sum_fours = downcast_value!(states[4], Float64Array);
+
+        for i in 0..counts.len() {
+            let c = counts.value(i);
+            if c == 0 {
+                continue;
+            }
+            self.count += c;
+            self.sum += sums.value(i);
+            self.sum_sqr += sum_sqrs.value(i);
+            self.sum_cub += sum_cubs.value(i);
+            self.sum_four += sum_fours.value(i);
+        }
+
+        Ok(())
+    }
+
+    fn evaluate(&mut self) -> Result<ScalarValue> {
+        if self.count <= 3 {
+            return Ok(ScalarValue::Float64(None));
+        }
+
+        let count_64 = 1_f64 / self.count as f64;
+        let m4 = count_64
+            * (self.sum_four - 4.0 * self.sum_cub * self.sum * count_64
+                + 6.0 * self.sum_sqr * self.sum.powi(2) * count_64.powi(2)
+                - 3.0 * self.sum.powi(4) * count_64.powi(3));
+
+        let m2 = (self.sum_sqr - self.sum.powi(2) * count_64) * count_64;
+        if m2 <= 0.0 {
+            return Ok(ScalarValue::Float64(None));
+        }
+
+        let count = self.count as f64;
+        let numerator = (count - 1.0) * ((count + 1.0) * m4 / m2.powi(2) - 3.0 * (count - 1.0));
+        let denominator = (count - 2.0) * (count - 3.0);
+
+        let target = numerator / denominator;
+
+        Ok(ScalarValue::Float64(Some(target)))
+    }
+
+    fn size(&self) -> usize {
+        std::mem::size_of_val(self)
+    }
+
+    fn state(&mut self) -> Result<Vec<ScalarValue>> {
+        Ok(vec![
+            ScalarValue::from(self.count),
+            ScalarValue::from(self.sum),
+            ScalarValue::from(self.sum_sqr),
+            ScalarValue::from(self.sum_cub),
+            ScalarValue::from(self.sum_four),
+        ])
+    }
+}

src/lib.rs

@@ -26,11 +26,13 @@ use datafusion::logical_expr::AggregateUDF;
 #[macro_use]
 pub mod macros;
 pub mod common;
+pub mod kurtosis;
 pub mod kurtosis_pop;
 pub mod max_min_by;
 pub mod mode;
 pub mod skewness;
 pub mod expr_extra_fn {
+    pub use super::kurtosis::kurtosis;
     pub use super::kurtosis_pop::kurtosis_pop;
     pub use super::max_min_by::max_by;
     pub use super::max_min_by::min_by;
@@ -43,6 +45,7 @@ pub fn all_extra_aggregate_functions() -> Vec<Arc<AggregateUDF>> {
         mode_udaf(),
         max_min_by::max_by_udaf(),
         max_min_by::min_by_udaf(),
+        kurtosis::kurtosis_udaf(),
         skewness::skewness_udaf(),
         kurtosis_pop::kurtosis_pop_udaf(),
     ]

tests/main.rs

@@ -364,3 +364,74 @@ async fn test_skewness() {
         - +-------------------+
     "###);
 }
+
+#[tokio::test]
+async fn test_kurtosis() {
+    let mut execution = TestExecution::new().await.unwrap();
+
+    let actual = execution
+        .run_and_format("SELECT kurtosis(col) FROM VALUES (1.0), (10.0), (100.0), (10.0), (1.0) as tab(col);")
+        .await;
+
+    insta::assert_yaml_snapshot!(actual, @r###"
+          - +-------------------+
+          - "| kurtosis(tab.col) |"
+          - +-------------------+
+          - "| 4.777292927667962 |"
+          - +-------------------+
+    "###);
+
+    let actual = execution
+        .run_and_format("SELECT kurtosis(col) FROM VALUES ('1'), ('10'), ('100'), ('10'), ('1') as tab(col);")
+        .await;
+
+    insta::assert_yaml_snapshot!(actual, @r###"
+          - +-------------------+
+          - "| kurtosis(tab.col) |"
+          - +-------------------+
+          - "| 4.777292927667962 |"
+          - +-------------------+
+    "###);
+
+    let actual = execution
+        .run_and_format("SELECT kurtosis(col) FROM VALUES (1.0), (2.0), (3.0) as tab(col);")
+        .await;
+
+    insta::assert_yaml_snapshot!(actual, @r###"
+          - +-------------------+
+          - "| kurtosis(tab.col) |"
+          - +-------------------+
+          - "|                   |"
+          - +-------------------+
+    "###);
+
+    let actual = execution.run_and_format("SELECT kurtosis(1);").await;
+
+    insta::assert_yaml_snapshot!(actual, @r###"
+          - +--------------------+
+          - "| kurtosis(Int64(1)) |"
+          - +--------------------+
+          - "|                    |"
+          - +--------------------+
+    "###);
+
+    let actual = execution.run_and_format("SELECT kurtosis(1.0);").await;
+
+    insta::assert_yaml_snapshot!(actual, @r###"
+          - +----------------------+
+          - "| kurtosis(Float64(1)) |"
+          - +----------------------+
+          - "|                      |"
+          - +----------------------+
+    "###);
+
+    let actual = execution.run_and_format("SELECT kurtosis(null);").await;
+
+    insta::assert_yaml_snapshot!(actual, @r###"
+          - +----------------+
+          - "| kurtosis(NULL) |"
+          - +----------------+
+          - "|                |"
+          - +----------------+
+    "###);
+}