KURT_q

Updated 2023-10-31 14:42:35.743000

Syntax

SELECT [westclintech].[wct].[KURT_q] (
   <@K_RangeQuery, nvarchar(4000),>)

Description

Use the scalar function KURT_q to calculate the kurtosis of a dataset. Kurtosis measures the peakedness of a distribution. Kurtosis is computed by taking the fourth moment of a distribution. A high kurtosis has a sharper peak and fatter tails, while a low kurtosis has a more rounded peak and shorter thinner tails. The equation for kurtosis is:

\frac{(n+1)n}{(n-1)(n-2)(n-3)}\frac{\sum_{i=1}^n(x-\bar{x})^4}{k_2^2} - 3\frac{(n-1)^2}{(n-2)(n-3)}

Arguments

@K_RangeQuery

the select statement, as text, used to determine the values to be used in the KURT_q calculation.

Return Type

float

Remarks

If there are fewer than four data points or if the standard deviation of the sample equal zero, KURT_q returns an error.

No GROUP BY is required for this function even though it produces aggregated results.

Examples

CREATE TABLE #k1

(

    [num] [float] NOT NULL

);

INSERT INTO #k1

VALUES

(91.3698);

INSERT INTO #k1

VALUES

(76.3382);

INSERT INTO #k1

VALUES

(74.5692);

INSERT INTO #k1

VALUES

(85.2957);

INSERT INTO #k1

VALUES

(99.0112);

INSERT INTO #k1

VALUES

(86.99);

INSERT INTO #k1

VALUES

(70.7837);

INSERT INTO #k1

VALUES

(72.834);

INSERT INTO #k1

VALUES

(78.1644);

INSERT INTO #k1

VALUES

(77.7472);

INSERT INTO #k1

VALUES

(66.0627);

INSERT INTO #k1

VALUES

(59.781);

INSERT INTO #k1

VALUES

(68.4793);

INSERT INTO #k1

VALUES

(78.6103);

INSERT INTO #k1

VALUES

(59.8621);

select wct.KURT_q('select num from #k1');

This produces the following result

{"columns":[{"field":"column 1","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"}],"rows":[{"column 1":""},{"column 1":"-0.0704978735822985"}]}