KURTOSIS_S

Updated 2023-10-23 20:19:10.643000

Syntax

SELECT [westclintech].[wct].[KURTOSIS_S] (
  <@Known_x, float,>)

Description

Use the aggregate function KURTOSIS_S to calculate the sample kurtosis. The KURTOSIS_S function is an implementation of the EXCEL KURT function.

G_2=\frac{(n+1)n}{(n-1)(n-2)(n-3)}\frac{\mu_4}{(\frac{\mu_2}{(n-1)})^2-3

Arguments

@Known_x

the values to be used in the calculation. @Known_x must be of a type float or of a type that implicitly converts to float.

Return Type

float

Remarks

If you want measure the kurtosis for a population, then use the KURTOSIS_P function.

To calculate the population skewness use the SKEWNESS_P function.

To calculate the sample skewness use the SKEWNESS_S function.

Examples

SELECT wct.KURTOSIS_S(x) as KURTOSIS_S
FROM
(
    SELECT 30000.0000216303
    UNION ALL
    SELECT 30000.0000565854
    UNION ALL
    SELECT 30000.000038137
    UNION ALL
    SELECT 30000.0000495983
    UNION ALL
    SELECT 30000.0000185861
    UNION ALL
    SELECT 30000.0000863479
    UNION ALL
    SELECT 30000.0000776366
    UNION ALL
    SELECT 30000.0000637985
    UNION ALL
    SELECT 30000.0000939786
    UNION ALL
    SELECT 30000.000031191
    UNION ALL
    SELECT 30000.0000550457
    UNION ALL
    SELECT 30000.0000207558
    UNION ALL
    SELECT 30000.0000805531
    UNION ALL
    SELECT 30000.0000241287
) n(x);

This produces the following result

{"columns":[{"field":"KURTOSIS_S","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"}],"rows":[{"KURTOSIS_S":"-1.39012610593176"}]}

In this example, we generate 100 random numbers form the standard normal distribution using the SeriesFloat function and calculate the population kurtosis.

SELECT wct.KURTOSIS_S(k.SeriesValue) as KURTOSIS_S
FROM wctMath.wct.SeriesFloat(0, 1, NULL, 100, 'N') k;

This produces the following result (your results will be different).

{"columns":[{"field":"KURTOSIS_S","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"}],"rows":[{"KURTOSIS_S":"0.491294825229997"}]}