Updated: 30 June 2013

Use RunningSKEW_S to calculate the samples skewness of column values in an ordered resultant table, without the need for a self-join. The sample skewness is calculated over all the values from the first value to the last value in the ordered group or partition. If the column values are presented to the functions out of order, an error message will be generated.

SELECT [westclintech].[wct].[RunningSKEW_S](

<@X, float,>

,<@RowNum, int,>

,<@Id, tinyint,>)

the value passed into the function. *@X* is an expression of type **float** or of a type that can be implicitly converted to **float**.

the number of the row within the group for which the sample skewness is being calculated. If *@RowNum* for the current row in a set is less than or equal to the previous *@RowNum* and *@RowNum* is not equal to 1, an error message will be generated.* @RowNum* is an expression of type **int** or of a type that can be implicitly converted to **int**.

a unique identifier for the RunningSKEW_S calculation. *@Id* allows you to specify multiple running sample skewness calculations within a resultant table. *@Id* is an expression of type **tinyint** or of a type that can be implicitly converted to **tinyint**.

· If *@Id* is NULL then *@Id* = 0.

· To calculate moving sample skewness, use the MovingSKEW_S function.

· To calculate the samples skewness for an entire data set, use the SKEWNESS_S function.

· If *@RowNum* is equal to 1, RunningSKEW_S is equal to zero.

· *@RowNum* must be in ascending order.

· There may be cases where the order in which the data are returned to the function and the order in which the results are returned are different, generally due to parallelism. You can use OPTION(MAXDOP 1) or OPTION(MAXDOP 1,FORCE ORDER) to help eliminate this problem

In this example, we have 20 rows of data and we want to caculate the sample skewness of x and y starting from the first row. Note that the *@Id* value for each RunningSKEW_S column is different.

SELECT rn

,x

,y

,wct.RunningSKEW_S(x,rn,NULL) as [SKEW_S x]

,wct.RunningSKEW_S(y,rn,1) as [SKEW_S y]

FROM (

SELECT 1,101,117 UNION ALL

SELECT 2,91,97 UNION ALL

SELECT 3,96,121 UNION ALL

SELECT 4,96,103 UNION ALL

SELECT 5,86,74 UNION ALL

SELECT 6,95,80 UNION ALL

SELECT 7,91,105 UNION ALL

SELECT 8,102,72 UNION ALL

SELECT 9,94,108 UNION ALL

SELECT 10,110,94 UNION ALL

SELECT 11,121,85 UNION ALL

SELECT 12,115,90 UNION ALL

SELECT 13,112,96 UNION ALL

SELECT 14,100,97 UNION ALL

SELECT 15,124,106 UNION ALL

SELECT 16,92,61 UNION ALL

SELECT 17,92,107 UNION ALL

SELECT 18,139,92 UNION ALL

SELECT 19,95,101 UNION ALL

SELECT 20,90,104

)n(rn,x,y)

This produces the following result.

rn x y SKEW_S x SKEW_S y

---- ----------- ----------- ---------------------- ----------------------

1 101 117 NULL NULL

2 91 97 NULL NULL

3 96 121 0 -1.54539252569502

4 96 103 0 -0.129678815660363

5 86 74 -0.404796008910937 -0.864550209720427

6 95 80 -0.547871643589439 -0.179587851309796

7 91 105 -0.179812666650057 -0.384309637141166

8 102 72 -0.183091963166347 -0.0994544316100886

9 94 108 -0.124285714285715 -0.331171026292888

10 110 94 0.709070384461684 -0.265262411674906

11 121 85 1.2958445379977 -0.0584746272003931

12 115 90 0.893378681947106 0.0476461160613627

13 112 96 0.618377295780968 0.0401051990837308

14 100 97 0.653762183949444 0.0164309317695287

15 124 106 0.625574752271121 -0.119264289357361

16 92 61 0.731016831476697 -0.359228636579172

17 92 107 0.828122509715119 -0.47105159705444

18 139 92 1.16094637809343 -0.446870439048321

19 95 101 1.24572587647292 -0.518472653357385

20 90 104 1.30010690278267 -0.602170891442928