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Add doc for covar/corr etc funtion (StarRocks#6118) (StarRocks#6268)
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* Add doc for covar/corr etc funtion
Signed-off-by: before-Sunrise <unclejyj@gmail.com>
---------

Signed-off-by: before-Sunrise <unclejyj@gmail.com>
Co-authored-by: evelyn.zhaojie <everlyn.zhaojie@gmail.com>
(cherry picked from commit c3f1994)

Co-authored-by: before-Sunrise <71162020+before-Sunrise@users.noreply.github.com>
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359 changes: 355 additions & 4 deletions sql-reference/sql-functions/Window_function.md
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当前 StarRocks 支持的窗口函数包括：

* `MIN()`, `MAX()`, `COUNT()`, `SUM()`, `AVG()`
* `FIRST_VALUE()`, `LAST_VALUE()`, `LEAD()`, `LAG()`
* `ROW_NUMBER()`, `RANK()`, `DENSE_RANK()`, `QUALIFY()`
* `NTILE()`
* MIN(), MAX(), COUNT(), SUM(), AVG()
* FIRST_VALUE(), LAST_VALUE(), LEAD(), LAG()
* ROW_NUMBER(), RANK(), DENSE_RANK(), QUALIFY()
* NTILE()
* VARIANCE(), VAR_SAMP(), STD(), STDDEV_SAMP(), COVAR_SAMP(), COVAR_POP(), CORR()

## 窗口函数语法及参数

Expand Down Expand Up @@ -824,3 +825,353 @@ from int_t where property in ('odd','even');
| 7 | odd | 21 |
+----+----------+--------------+
~~~

## 使用 VARIANCE, VAR_POP, VARIANCE_POP 窗口函数

VARIANCE() 窗口函数用于统计表达式的总体方差。VAR_POP 和 VARIANCE_POP 是 VARIANCE 窗口函数的别名。

**语法：**

~~~SQL
VARIANCE(expression) [OVER (partition_by_clause)]
~~~

> 注意
>
> `VARIANCE()` 函数只支持 PARTITION BY，不支持 ORDER BY 和 Window 子句。
**参数说明：**

当表达式expression为列值时，支持以下数据类型: TINYINT、SMALLINT、INT、BIGINT、LARGEINT、FLOAT、DOUBLE、DECIMAL

**示例：**

假设表 `agg` 有以下数据：

```plaintext
mysql> select * from agg;
+------+-------+-------+
| no | k | v |
+------+-------+-------+
| 1 | 10.00 | NULL |
| 2 | 10.00 | 11.00 |
| 2 | 20.00 | 22.00 |
| 2 | 25.00 | NULL |
| 2 | 30.00 | 35.00 |
+------+-------+-------+
```

使用 VARIANCE() 窗口函数。

```plaintext
mysql> select variance(k) over (partition by no) FROM agg;
+-------------------------------------+
| variance(k) OVER (PARTITION BY no ) |
+-------------------------------------+
| 0 |
| 54.6875 |
| 54.6875 |
| 54.6875 |
| 54.6875 |
+-------------------------------------+
```

## 使用 VAR_SAMP, VARIANCE_SAMP 窗口函数

VAR_SAMP() 窗口函数用于统计表达式的样本方差。

**语法：**

```sql
VAR_SAMP(expression) [OVER (partition_by_clause)]
```

> 注意
>
> VAR_SAMP() 函数只支持 PARTITION BY，不支持 ORDER BY 和 Window 子句。
**参数说明：**

当表达式expression为列值时，支持以下数据类型: TINYINT、SMALLINT、INT、BIGINT、LARGEINT、FLOAT、DOUBLE、DECIMAL

**示例：**

假设表 `agg` 有以下数据：

```plaintext
mysql> select * from agg;
+------+-------+-------+
| no | k | v |
+------+-------+-------+
| 1 | 10.00 | NULL |
| 2 | 10.00 | 11.00 |
| 2 | 20.00 | 22.00 |
| 2 | 25.00 | NULL |
| 2 | 30.00 | 35.00 |
+------+-------+-------+
```

使用 VAR_SAMP() 窗口函数。

```plaintext
mysql> select VAR_SAMP(k) over (partition by no) FROM agg;
+-------------------------------------+
| var_samp(k) OVER (PARTITION BY no ) |
+-------------------------------------+
| 0 |
| 72.91666666666667 |
| 72.91666666666667 |
| 72.91666666666667 |
| 72.91666666666667 |
+-------------------------------------+
```

## 使用 STD, STDDEV, STDDEV_POP 窗口函数

STD() 窗口函数用于统计表达式的总体标准差。

**语法：**

```sql
STD(expression) [OVER (partition_by_clause)]
```

> 注意
>
> STD() 函数只支持 PARTITION BY，不支持 ORDER BY 和 Window 子句。
**参数说明：**

当表达式expression为列值时，支持以下数据类型: TINYINT、SMALLINT、INT、BIGINT、LARGEINT、FLOAT、DOUBLE、DECIMAL

**示例：**

假设表 `agg` 有以下数据：

```plaintext
mysql> select * from agg;
+------+-------+-------+
| no | k | v |
+------+-------+-------+
| 1 | 10.00 | NULL |
| 2 | 10.00 | 11.00 |
| 2 | 20.00 | 22.00 |
| 2 | 25.00 | NULL |
| 2 | 30.00 | 35.00 |
+------+-------+-------+
```

使用 STD() 窗口函数。

```plaintext
mysql> select STD(k) over (partition by no) FROM agg;
+--------------------------------+
| std(k) OVER (PARTITION BY no ) |
+--------------------------------+
| 0 |
| 7.39509972887452 |
| 7.39509972887452 |
| 7.39509972887452 |
| 7.39509972887452 |
+--------------------------------+
```

## 使用 STDDEV_SAMP 窗口函数

STDDEV_SAMP() 窗口函数用于统计表达式的样本标准差。

**语法：**

```sql
STDDEV_SAMP(expression) [OVER (partition_by_clause)]
```

> 注意
>
> STDDEV_SAMP() 函数只支持 PARTITION BY，不支持 ORDER BY 和 Window 子句。
**参数说明：**

当表达式expression为列值时，支持以下数据类型: TINYINT、SMALLINT、INT、BIGINT、LARGEINT、FLOAT、DOUBLE、DECIMAL

**示例：**

假设表 `agg` 有以下数据：

```plaintext
mysql> select * from agg;
+------+-------+-------+
| no | k | v |
+------+-------+-------+
| 1 | 10.00 | NULL |
| 2 | 10.00 | 11.00 |
| 2 | 20.00 | 22.00 |
| 2 | 25.00 | NULL |
| 2 | 30.00 | 35.00 |
+------+-------+-------+
```

使用 STDDEV_SAMP() 窗口函数。

```plaintext
mysql> select STDDEV_SAMP(k) over (partition by no) FROM agg;
+----------------------------------------+
| stddev_samp(k) OVER (PARTITION BY no ) |
+----------------------------------------+
| 0 |
| 8.539125638299666 |
| 8.539125638299666 |
| 8.539125638299666 |
| 8.539125638299666 |
+----------------------------------------+
```

## 使用 COVAR_SAMP 窗口函数

COVAR_SAMP() 窗口函数用于统计表达式的样本协方差。

**语法：**

```sql
COVAR_SAMP(expression) [OVER (partition_by_clause)]
```

> 注意
>
> COVAR_SAMP() 函数只支持 PARTITION BY，不支持 ORDER BY 和 Window 子句。
**参数说明：**

当表达式expression为列值时，支持以下数据类型: TINYINT、SMALLINT、INT、BIGINT、LARGEINT、FLOAT、DOUBLE、DECIMAL

**示例：**

假设表 `agg` 有以下数据：

```plaintext
mysql> select * from agg;
+------+-------+-------+
| no | k | v |
+------+-------+-------+
| 1 | 10.00 | NULL |
| 2 | 10.00 | 11.00 |
| 2 | 20.00 | 22.00 |
| 2 | 25.00 | NULL |
| 2 | 30.00 | 35.00 |
+------+-------+-------+
```

使用 COVAR_SAMP() 窗口函数。

```plaintext
mysql> select COVAR_SAMP(k, v) over (partition by no) FROM agg;
+------------------------------------------+
| covar_samp(k, v) OVER (PARTITION BY no ) |
+------------------------------------------+
| NULL |
| 119.99999999999999 |
| 119.99999999999999 |
| 119.99999999999999 |
| 119.99999999999999 |
+------------------------------------------+
```

## 使用 COVAR_POP 窗口函数

COVAR_POP() 窗口函数用于统计表达式的总体协方差。

**语法：**

```sql
COVAR_POP(expression, expression) [OVER (partition_by_clause)]
```

> 注意
>
> COVAR_POP() 函数只支持 PARTITION BY，不支持 ORDER BY 和 Window 子句。
**参数说明：**

当表达式expression为列值时，支持以下数据类型: TINYINT、SMALLINT、INT、BIGINT、LARGEINT、FLOAT、DOUBLE、DECIMAL

**示例：**

假设表 `agg` 有以下数据：

```plaintext
mysql> select * from agg;
+------+-------+-------+
| no | k | v |
+------+-------+-------+
| 1 | 10.00 | NULL |
| 2 | 10.00 | 11.00 |
| 2 | 20.00 | 22.00 |
| 2 | 25.00 | NULL |
| 2 | 30.00 | 35.00 |
+------+-------+-------+
```

使用 COVAR_POP() 窗口函数。

```plaintext
mysql> select COVAR_POP(k, v) over (partition by no) FROM agg;
+-----------------------------------------+
| covar_pop(k, v) OVER (PARTITION BY no ) |
+-----------------------------------------+
| NULL |
| 79.99999999999999 |
| 79.99999999999999 |
| 79.99999999999999 |
| 79.99999999999999 |
+-----------------------------------------+
```

## 使用 CORR 窗口函数

CORR() 窗口函数用于统计表达式的相关系数。

**语法：**

```sql
CORR(expression, expression) [OVER (partition_by_clause)]
```

> 注意
>
> CORR() 函数只支持 PARTITION BY，不支持 ORDER BY 和 Window 子句。
**参数说明：**

当表达式expression为列值时，支持以下数据类型: TINYINT、SMALLINT、INT、BIGINT、LARGEINT、FLOAT、DOUBLE、DECIMAL

**示例：**

假设表 `agg` 有以下数据：

```plaintext
mysql> select * from agg;
+------+-------+-------+
| no | k | v |
+------+-------+-------+
| 1 | 10.00 | NULL |
| 2 | 10.00 | 11.00 |
| 2 | 20.00 | 22.00 |
| 2 | 25.00 | NULL |
| 2 | 30.00 | 35.00 |
+------+-------+-------+
```

使用 CORR() 窗口函数。

```plaintext
mysql> select CORR(k, v) over (partition by no) FROM agg;
+------------------------------------+
| corr(k, v) OVER (PARTITION BY no ) |
+------------------------------------+
| NULL |
| 0.9988445981121532 |
| 0.9988445981121532 |
| 0.9988445981121532 |
| 0.9988445981121532 |
+------------------------------------+
```
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