Docs for skew and kurt

docs/sql-manual/sql-functions/aggregate-functions/kurt.md

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+---
+{
+ "title": "KURT,KURT_POP,KURTOSIS",
+ "language": "en"
+}
+---
+
+<!-- 
+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.
+-->
+
+## Description
+
+Returns the [kurtosis](https://en.wikipedia.org/wiki/Kurtosis) of the expr expression.
+The forumula used for this function is `4-th centrol moment / ((variance)^2) - 3`, when variance is zero, `kurtosis` will return `NULL`.
+
+## Syntax
+
+`kurtosis(expr)`
+
+## Arguments
+
+TinyInt/SmallInt/Integer/BigInt/Float/Double, Decimal will be casted to a float number.
+
+## Return value
+
+`Double`
+
+## Example
+```sql
+create table statistic_test(tag int, val1 double not null, val2 double null) distributed by hash(tag) properties("replication_num"="1")
+
+insert into statistic_test values (1, -10, -10),(2, -20, NULL),(3, 100, NULL),(4, 100, NULL),(5, 1000,1000);
+
+// NULL is ignored
+select kurt(val1), kurt(val2) from statistic_test
+--------------
+
++-------------------+--------------------+
+| kurt(val1) | kurt(val2) |
++-------------------+--------------------+
+| 0.162124583734851 | -1.3330994719286338 |
++-------------------+--------------------+
+1 row in set (0.02 sec)
+
+// Each group just has one row, result is NULL
+select kurt(val1), kurt(val2) from statistic_test group by tag
+--------------
+
++------------+------------+
+| kurt(val1) | kurt(val2) |
++------------+------------+
+| NULL | NULL |
+| NULL | NULL |
+| NULL | NULL |
+| NULL | NULL |
+| NULL | NULL |
++------------+------------+
+5 rows in set (0.02 sec)
+```
+
+## Related Commands
+
+[skew](./skew.md)

docs/sql-manual/sql-functions/aggregate-functions/skew.md

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+---
+{
+ "title": "SKEW,SKEW_POP,SKEWNESS",
+ "language": "en"
+}
+---
+
+<!-- 
+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.
+-->
+
+## skewness,skew,skew_pop
+### Description
+
+Returns the [skewness](https://en.wikipedia.org/wiki/Skewness) of the expr expression.
+The forumula used for this function is `3-th centrol moment / ((variance)^{1.5})`, when variance is zero, `skewness` will return `NULL`.
+
+### Syntax
+
+`skewness(expr)`
+
+### Arguments
+
+TinyInt/SmallInt/Integer/BigInt/Float/Double, Decimal will be casted to a float number.
+
+### Return value
+
+`Double`
+
+### Example
+```sql
+create table statistic_test (tag int, val1 double not null, val2 double null)
+ distributed by hash(tag) properties("replication_num"="1")
+
+insert into statistic_test values (1, -10, -10),
+ (2, -20, NULL),
+ (3, 100, NULL),
+ (4, 100, NULL),
+ (5, 1000,1000);
+
+// NULL is ignored
+select skew(val1), skew(val2) from statistic_test
+--------------
+
++--------------------+--------------------+
+| skew(val1) | skew(val2) |
++--------------------+--------------------+
+| 1.4337199628825619 | 1.1543940205711711 |
++--------------------+--------------------+
+1 row in set (0.01 sec)
+
+// Each group just has one row, result is NULL
+select skew(val1), skew(val2) from statistic_test group by tag
+--------------
+
++------------+------------+
+| skew(val1) | skew(val2) |
++------------+------------+
+| NULL | NULL |
+| NULL | NULL |
+| NULL | NULL |
+| NULL | NULL |
+| NULL | NULL |
++------------+------------+
+5 rows in set (0.04 sec)
+```
+### Related Commands
+
+[kurt](./kurt.md)

i18n/zh-CN/docusaurus-plugin-content-docs/current/sql-manual/sql-functions/aggregate-functions/kurt.md

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+---
+{
+ "title": "KURT,KURT_POP,KURTOSIS",
+ "language": "zh-CN"
+}
+---
+
+<!-- 
+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.
+-->
+
+## 描述
+
+kurtosis 返回 expr 表达式的[峰度值](https://en.wikipedia.org/wiki/Kurtosis)。此函数使用的公式为 第四阶中心矩 / (方差的平方) - 3，当方差为零时，kurtosis 将返回 NULL。
+
+## 语法
+
+`kurtosis(expr)`
+
+## 参数说明
+
+TinyInt/SmallInt/Integer/BigInt/Float/Double, Decimal 会被 cast 成浮点数参与运算。
+
+## 返回值说明
+
+`Double`
+
+## 举例
+```sql
+create table statistic_test(tag int, val1 double not null, val2 double null) distributed by hash(tag) properties("replication_num"="1");
+
+insert into statistic_test values (1, -10, -10),(2, -20, NULL),(3, 100, NULL),(4, 100, NULL),(5, 1000,1000);
+
+// NULL 值会被忽略
+select kurt(val1), kurt(val2) from statistic_test;
+--------------
+
++-------------------+--------------------+
+| kurt(val1) | kurt(val2) |
++-------------------+--------------------+
+| 0.162124583734851 | -1.3330994719286338 |
++-------------------+--------------------+
+1 row in set (0.02 sec)
+
+// 每组只有一行数据，结果为 NULL
+select kurt(val1), kurt(val2) from statistic_test group by tag;
+--------------
+
++------------+------------+
+| kurt(val1) | kurt(val2) |
++------------+------------+
+| NULL | NULL |
+| NULL | NULL |
+| NULL | NULL |
+| NULL | NULL |
+| NULL | NULL |
++------------+------------+
+5 rows in set (0.02 sec)
+```
+
+## 相关命令
+
+[skew](./skew.md)

i18n/zh-CN/docusaurus-plugin-content-docs/current/sql-manual/sql-functions/aggregate-functions/skew.md

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+---
+{
+ "title": "SKEW,SKEW_POP,SKEWNESS",
+ "language": "en"
+}
+---
+
+<!-- 
+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.
+-->
+
+## skewness,skew,skew_pop
+### 描述
+
+返回表达式的 [斜度](https://en.wikipedia.org/wiki/Skewness)。
+用来计算斜度的公式是 `3阶中心矩 / ((方差)^{1.5})`, 当方差为零时, `skewness` 会返回 `NULL`.
+
+### 语法
+
+`skewness(expr)`
+
+### 参数说明
+
+TinyInt/SmallInt/Integer/BigInt/Float/Double, Decimal 会被 cast 成浮点数参与运算。
+
+### 返回值说明
+
+`Double`
+
+### 举例
+```sql
+create table statistic_test (tag int, val1 double not null, val2 double null)
+ distributed by hash(tag) properties("replication_num"="1")
+
+insert into statistic_test values (1, -10, -10),
+ (2, -20, NULL),
+ (3, 100, NULL),
+ (4, 100, NULL),
+ (5, 1000,1000);
+
+// NULL is ignored
+select skew(val1), skew(val2) from statistic_test
+--------------
+
++--------------------+--------------------+
+| skew(val1) | skew(val2) |
++--------------------+--------------------+
+| 1.4337199628825619 | 1.1543940205711711 |
++--------------------+--------------------+
+1 row in set (0.01 sec)
+
+// Each group just has one row, result is NULL
+select skew(val1), skew(val2) from statistic_test group by tag
+--------------
+
++------------+------------+
+| skew(val1) | skew(val2) |
++------------+------------+
+| NULL | NULL |
+| NULL | NULL |
+| NULL | NULL |
+| NULL | NULL |
+| NULL | NULL |
++------------+------------+
+5 rows in set (0.04 sec)
+```
+### 相关命令
+
+[kurt](./kurt.md)