Updated: 30 June 2013

Use RunningKURT_S to calculate the sample kurtosis of column values in an ordered resultant table, without the need for a self-join. The sample kurtosis 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].[RunningKURT_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 kurtosis 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 RunningKURT_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 kurtosis, use the MovingKURT_S function.

· To calculate the sample kurtosis for an entire data set, use the KURTOSIS_S function.

· If *@RowNum* is equal to 1, RunningKURT_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 kurtosis of x and y starting from the first row. Note that the *@Id* value for each RunningKURT_S column is different.

SELECT rn

,x

,y

,wct.RunningKURT_S(x,rn,NULL) as [KURT_S x]

,wct.RunningKURT_S(y,rn,1) as [KURT_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 KURT_S x KURT_S y

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

1 101 117 NULL NULL

2 91 97 NULL NULL

3 96 121 NULL NULL

4 96 103 1.5 -4.11489694128959

5 86 74 -0.177514792899409 0.389212884542543

6 95 80 0.653089374822509 -1.70637468912197

7 91 105 0.238796694436977 -1.07718583354361

8 102 72 -0.446379105658887 -1.63506342871445

9 94 108 -0.0668571428571463 -1.40746937458679

10 110 94 0.9035183955179 -1.14057778810637

11 121 85 1.80974330712932 -1.17954713149457

12 115 90 -0.00554937100889941 -0.997578017618969

13 112 96 -0.6802006038621 -0.767217614514457

14 100 97 -0.44238457089804 -0.554922326554543

15 124 106 -0.685738954145421 -0.53957325173014

16 92 61 -0.56349975591933 -0.31799220337797

17 92 107 -0.419582246269193 -0.255917838308746

18 139 92 0.854487881313605 -0.115157025183854

19 95 101 1.09029070734079 0.0477693152924239

20 90 104 1.22585595223078 0.175899602607029